Ch - PC\|MAC



Foundations for Geometry

Section 1.1 A Entrance Quiz

Choose the best answer.

Refer to the figure for Exercises 1 and 2.

[pic]

1. Which represents the name of the ray whose endpoint is K and that passes through R?

A [pic] C [pic]

B [pic] D [pic]

2. In the diagram, how many different rays have endpoint R?

F 1 H 3

G 2 J 4

Refer to the figure for Exercises 3 and 4.

[pic]

3. Which line contains points S and U?

A line m C line p

B line n D [pic]

4. In the diagram, how many different segments can be named?

F 0 H 2

G 1 J 3

Refer to the figure for Exercises 5 and 6.

[pic]

5. What is MP?

A 1 C 4

B 2 D 5

6. What is LP?

F (7.5 H 2.5

G (2.5 J 7.5

7. Write below, in your own words, the description of a point, line, and plane.

Foundations for Geometry

Section B Quiz

Choose the best answer.

1. What is the perimeter of a rectangle whose width is (x ( 7) units and whose length is (3x ( 10) units?

[pic]

A (2x ( 17) units C (4x ( 34) units

B (4x ( 3) units D (8x ( 6) units

2. To the nearest whole number, what is the area of this circle?

[pic]

F 1,810 in2 H 113 in2

G 452 in2 J 38 in2

3. To the nearest tenth, what is the circumference of a circle whose

diameter is 8 meters?

A 201.1 m C 25.1 m

B 50.2 m D 12.6 m

4. Find the coordinates for the midpoint

of [pic] with endpoints M((3, 8) and

N((7, 6).

F ((5, 7) H (2, 1)

G (5, (7) J ((2, (1)

5. K is the midpoint of [pic], P has coordinates ((9, (4), and K

has coordinates ((1, 6). What

are the coordinates of Q?

A ((5, 1) C ((11, 8)

B (5, 10) D (7, 16)

6. What is the distance, to the nearest

whole number, from K(5, 6) to P(1, (4)?

[pic]

F 14 H 11

G 13 J 6

7. Which best describes the transformation?

[pic]

A preimage C rotation

B reflection D translation

8. A figure has vertices at K(5, 5),

L(5, 3), M(1, 1), and N(3, 5). After a transformation, the image of the figure has vertices at K'((5, (5), L'((3, (5), M'((1, (1), and N'((5, (3). Which best describes the transformation?

F preimage H rotation

G reflection J translation

Geometric Reasoning

Section A Quiz

Choose the best answer.

1. What is the next letter in the sequence?

D, H, L, P, . . .

A Q C S

B R D T

2. Which is the counterexample that proves the conjecture false?

“If two rays have the same endpoint, then they are opposite rays.”

F [pic] H [pic]

G [pic] J [pic]

3. Identify the hypothesis of the conditional statement “Two angles are complementary if the sum of their measures is 90 degrees.”

A if

B Two angles are complementary

C the sum of their measures is

90 degrees

D Two angles are complementary if the sum of their measures is 90 degrees.

4. Which conditional statement has the same truth value as this statement?

“The sum of two odd numbers is even.”

F If two even numbers are added, then their sum is even.

G If an even and odd number are added, then their sum is even.

H If two even numbers are multiplied, then their product is odd.

J If two odd numbers are multiplied, then their product is even.

5. What is the inverse of the statement

“If two coplanar lines do not intersect, then they are parallel”?

A If two coplanar lines do not intersect, then they are not parallel.

B If two coplanar lines intersect, then they are not parallel.

C If two lines are parallel, then they are coplanar and do not intersect.

D If two coplanar lines are not parallel, then they intersect.

6. Which conjecture is valid by the Law of Syllogism for the following scenario?

“If Joe buys Nancy a card, he will give it to her. If Nancy is having a birthday, then Joe will buy her a card.”

F If Nancy is having a birthday, then Joe will give her a card.

G If Joe buys Nancy a card, then she

is having a birthday.

H If Joe gives Nancy a card, then he bought the card.

J If Joe gives Nancy a card, then she

is having a birthday.

7. Consider the related biconditional statement for the conditional statement “If Shelly lives in Texas, then she lives in the United States.”

Which of the following statements is true about the related biconditional statement?

A The biconditional is true because the conditional is true.

B The biconditional is false because the conditional and its converse are false.

C The biconditional is true because the conditional and its converse are true.

D The biconditional is false because the converse of the conditional is false.

Geometric Reasoning

Section B Quiz

Choose the best answer.

1. If r + 14 ’ −9, what justifies r ’ −23?

A Transitive Property of Equality

B Subtraction Property of Equality

C Symmetric Property of Equality

D Reflexive Property of Equality

2. If [pic] ’ 8, what justifies x − 1 ’ 16?

F Subtraction Property of Equality

G Division Property of Equality

H Transitive Property of Equality

J Multiplication Property of Equality

3. If 5 ’ 2k, what justifies 2k ’ 5?

A Multiplication Property of Equality

B Division Property of Equality

C Symmetric Property of Equality

D Reflexive Property of Equality

4. Which completes the statement?

If 2a(a − 4) ’ 10, then ______ by

the Distributive Property.

F 2a(a − 4) − 10 ’ 0

G a ’ 5 or −1

H a(a − 4) ’ 5

J 2a2 − 8a ’ 10

5. Which completes the statement?

If 6x ’ 5 and d ’ 6x, then ______ by

the Transitive Property of Equality.

A d ’ 5 C 6x ’ d

B x ’ [pic] D x ’ [pic]

6. Which completes the statement?

If [pic] then ______ by the Symmetric Property of Congruence.

F RS ’ GH H [pic]

G [pic] J [pic]

7. Given: L bisects [pic]; M bisects [pic]

Prove: KL ’ MN

[pic]

Proof:

Since L bisects [pic] and M bisects [pic] by definition of bisect, [pic] and

[pic] Then, by the      ?     ,

[pic] Finally, KL ’ MN by the definition of congruent segments.

Which completes the proof?

A Common Segments Theorem

B Transitive Property of Congruence

C Segment Addition Postulate

D Symmetric Property of Congruence

8. Given: ∠1 ” ∠4

Prove: ∠2 ” ∠3

Proof:

|Statements |Reasons |

|1. ∠1 ” ∠4 |1. Given |

|2. ∠1 and ∠2 are supp., |2. Lin. Pairs |

|and ∠3 and ∠4 are |Thm. |

|supp. | |

|3. ∠2 ” ∠3 |3.      ?      |

Which completes the proof?

F Transitive Property of Congruence

G Vertical Angles Theorem

H Congruent Supplements Theorem

J Angle Addition Postulate

9. For the following statement, what is the “Prove” statement?

If ABCD is a rhombus, then it is a parallelogram.

A ABCD is a quadrilateral.

B ABCD is a rhombus.

C ABCD is a parallelogram.

D ABCD is not a square.

Parallel and Perpendicular Lines

Section A Quiz

Choose the best answer.

Refer to the figure for Exercises 1–3.

[pic]

1. Which segment is perpendicular to [pic]?

A [pic] C [pic]

B [pic] D [pic]

2. Which segment is parallel to [pic]?

F [pic] H [pic]

G [pic] J [pic]

3. Which segment is NOT skew to [pic]?

A [pic] C [pic]

B [pic] D [pic]

Refer to the figure for Exercises 4 and 5.

[pic]

4. Which pair of angles are corresponding angles?

F (1 and (4 H (2 and (5

G (6 and (8 J (8 and (7

5. Which pair of angles are alternate exterior angles?

A (4 and (8 C (3 and (7

B (2 and (5 D (1 and (4

6. What is the value of x?

[pic]

F 35 H 15

G 20 J 12.5

7. Which could you use to show that u || v?

[pic]

A (1 and (8 are supplementary.

B (4 and (8 are supplementary.

C (3 and (7 are congruent.

D (7 and (8 are congruent.

8. Why is m ( n?

F If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

G If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.

H In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

J If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.

Parallel and Perpendicular Lines

Section B Quiz

Choose the best answer.

1. What is the slope of the line that passes through (4, 0) and (8, (1)?

A (4 C (12

B [pic] D [pic]

2. What is the slope of the line that passes through ((6, (4) and (9, (19)?

F [pic] H (1

G [pic] J (5

3. The slope of a line is [pic]. What is the slope of a line that is perpendicular to it?

A [pic] C [pic]

B [pic] D [pic]

4. What is the slope of a line parallel to the line that passes through (4, (3) and

(3, (1)?

F [pic] H [pic]

G 2 J (2

5. Which is the equation for the line having slope (6 that passes through (5, (5)?

A y ( (6x

B y ( (6x ( 5

C y ( 5 ( (6(x ( 5)

D y ( 5 ( (6(x ( 5)

6. Which is the equation for the line that passes through ((4, (3) and ((2, 3)?

F y ( 3x ( 15 H y ( (3x ( 15

G y ( 3x ( 9 J y ( (3x ( 9

7. Which is the graph of y ( 1 ( (2(x ( 3)?

A C

B D

8. Which equation represents the graph of the line that coincides with the graph of

[pic]?

F 6x ( 4y ( 36 H [pic]

G y ( 3 ( (9(x ( 2) J 2x ( 3y ( 9

9. The graph of which line intersects the graph of y ( 10 ( (5(x ( 1) in only one point?

A y ( 10 ( 5(x ( 1)

B y ( (5(x – 2)

C 5x ( y ( (5

D y ( 5((x ( 5)

10. The graph of which

equation is parallel

to the line in the

graph?

F 3x ( y ( 2

G y ( 1 ( (3(x ( 1)

H y ( 3x

J y ( (2x ( 3

Triangle Congruence

Section A Quiz

Choose the best answer.

1. The polygon Q(3, 2), R(6, 5), S(6, 2) undergoes the transformation:

(x, y) ( (4x, 4y). Name the coordinates

of the image points.

A Q'(3, 2), R'(6, 5), S'(6, 2)

B Q'(7, 6), R'(10, 9), S'(10, 6)

C Q'(12, 8), R'(24, 20), S'(24, 8)

D Q'(–1, –2), R'(2, 1), S'(2, –2)

2. The angles of a triangle measure 4°,

86°, and 90°. Which classification of

the triangle is correct?

F acute H obtuse

G equiangular J right

3. Which could be the angle measures

of an acute triangle?

A 32°-56°-92° C 34°-56°-90°

B 33°-58°-91° D 35°-56°-89°

4. What is the length of the longest side

of the triangle?

[pic]

F 8.5 H 19

G 26 J 40

5. What is m∠W ?

[pic]

A 35( C 70(

B 40.3( D 81(

6. Two angles of a triangle measure 22° and 53°. What is the measure of the

third angle?

F 15° H 75°

G 25° J 105°

7. What is the value of x if the acute angles of a right triangle measure 8x° and 12x°?

A 4.5 C 9

B 5 D 10

8. In the figure, (PQR ” (UVW. What is m∠R?

[pic]

F 42° H 88°

G 72° J 92°

9. If (KMQ ” (WJR, which segment is congruent to [pic]?

A [pic] C [pic]

B [pic] D [pic]

10. Which angle is congruent to ∠Z if

(ZLV ” ΔSPN ?

F ∠V H ∠N

G ∠S J ∠P

11. If ΔABC ” ΔKJC, which statement is NOT necessarily true?

[pic]

A ∠ACB ” ∠KCJ C [pic]

B ∠J ” ∠B D [pic]

12. Suppose ∠S ” ∠N, ∠J ” ∠I,

∠A ” ∠T, [pic] and

[pic] Which is true?

F ΔJSA ” ΔITN H ΔJSA ” ΔINT

G ΔJSA ” ΔNTI J ΔJSA ” ΔTNI

Triangle Congruence

Section B Quiz

Choose the best answer.

1. For which value of x is ΔRST ” ΔUVW ?

[pic]

A 2 C [pic]

B 4 D 12

2. What additional information is needed to prove ΔMNP ” ΔPQM by SAS?

[pic]

F ∠N ” ∠Q

G ∠MPN ” ∠MPQ

H [pic]

J [pic]

3. A parachute jumper called into the airport to be rescued by helicopter. She said her pilot flew 8 kilometers west and then headed due north about 20 minutes before she jumped. Does the helicopter pilot have enough information to locate her exact location?

A Yes, by AAS

B Yes, by SAS

C Yes, by HL

D No

4. Which CANNOT be used to prove

ΔMNK ” ΔKLM?

[pic]

F SAS H AAS

G ASA J HL

5. In the figure, H is the midpoint of [pic] and [pic] What reason can be used in a proof to show [pic]

[pic]

A AAS C Def. of bisects

B ASA D CPCTC

6. Which is the best position of a square with side length 5 for a coordinate proof?

F (5, 5), (10, 5), (10, 10), and (5, 10)

G (0, 0), (5, 0), (5, 5), and (0, 5)

H (1, 1), (6, 1), (6, 6), and (1, 6)

J (−3, 0), (2, 0), (2, 5), and (−3, 5)

7. How can coordinate proof be used to prove two lines are parallel?

A The product of their slopes is −1.

B The product of their slopes is 1.

C The slopes are the same.

D The y-intercepts are the same.

8. What is the measure of one of the base angles of an isosceles triangle if the measure of the vertex angle is 98°?

F 1° H 41°

G 2° J 82°

9. One angle of an equilateral triangle measures (4x − 20)°. What is the value of x?

A 2.5 C 12.5

B 10 D 20

10. Suppose ΔMWR ” ΔCYQ, MW ’ 8,

WR ’ 9, and CQ ’ 10. What is MR?

F 8 H 10

G 9 J 11

Properties and Attributes of Triangles

Section A Quiz

Choose the best answer.

1. [pic] is the perpendicular bisector of [pic] What is QN?

[pic]

A 7 C 14

B 10.5 D 28

2. If m∠LJK ’ 28°, what is m∠MLK?

[pic]

F 56° H 112°

G 62° J 124°

3. A segment has endpoints S(−4, −3) and T(2, −9). Which equation represents the perpendicular bisector of the segment?

A y + 6 ’ 1(x + 1)

B y + 9 ’ 1(x − 2)

C y + 3 ’ 1(x + 4)

D y + 3 ’ 1(x − 6)

4. Point Z is the circumcenter of (RST.

What is TZ?

[pic]

F 3 H 5

G 4 J 6

5. Point K is the incenter of (PQR.

What is m∠RKQ?

[pic]

A 100 C 125

B 115 D 130

6. Which must be true?

[pic]

F m∠PQY ’ m∠RQY

G m∠PRZ ’ m∠RPX

H JZ ’ JX

J QJ ’ 2 • JY

7. Where do the altitudes of (TUV meet?

[pic]

A (0, 2) C (0, 1)

B (0, 1.5) D (1.5, 1)

8. [pic] is a midsegment of (ABC.

Which statement is impossible?

[pic]

F AP ’ PC H [pic]

G PQ ’ BC J ∠A ( ∠APQ

Properties and Attributes of Triangles

Section B Quiz

Choose the best answer.

1. To prove indirectly that the base angles of an obtuse isosceles triangle must be acute, what is the best first step?

A Assume that the vertex angle is acute.

B Assume that the base angles are obtuse.

C Assume that the base angles are right angles.

D Assume that the base angles are not acute.

2. Two sides of a triangle are 11 centimeters and 14 centimeters. What are all possible values for the length x of the third side?

F x ’ 3 or x ’ 25 H x < 3 or x > 25

G 3 < x < 25 J x ’ 14

3. In ΔLMN, LM ’ 7, LN ’ 10, and

MN ’ 5. What can you conclude

about the angle measures?

A m∠L < m∠M < m∠N

B m∠M < m∠N < m∠L

C m∠L < m∠N < m∠M

D Not here

4. Which statement about n must be true?

[pic]

F n ’ 15 H 0 < n < 15

G n ’ 15 or J 15 < n < 49.5

n ’ 49.5

5. The hypotenuse of a right triangle measures 19 meters. One leg measures 15 meters. To the nearest tenth of a meter, what is the length of the other leg?

A 11.7 m C 24.2 m

B 17.0 m D 68.0 m

6. Which statement about r must be true?

[pic]

F [pic] H r < 3

G [pic] J [pic]

7. The sides of a triangle measure 7, 8, and 12. Which type of triangle is it?

A acute C obtuse

B equilateral D right

8. The sides of a triangle measure 16, 30, and 34. Which type of triangle is it?

F acute H obtuse

G equilateral J right

9. The hypotenuse of an isosceles right triangle is 36 units. To the nearest tenth, what is the length of one of the legs?

A 25.5 units C 8.5 units

B 18.0 units D 4.2 units

10. Each side of an equilateral triangle measures 11 centimeters. To the nearest tenth of a centimeter, what is the length of the altitude?

F 7.8 cm H 19.1 cm

G 9.5 cm J 22 cm

11. The longest side of a 30°-60°-90°

triangle measures 8. What is the

length of the longer leg?

A 8 C [pic]

B [pic] D 4

Polygons and Quadrilaterals

Section A Quiz

Choose the best answer.

1. Which must be a regular convex polygon?

A [pic] C [pic]

B [pic] D [pic]

2. Which is an irregular concave polygon?

F [pic] H [pic]

G [pic] J [pic]

3. The consecutive angles of a parallelogram measure (x + 30)° and 4x°. What is the measure of the smallest angle?

A 10° C 40°

B 30° D 60°

4. PQRS is a parallelogram. Find x.

[pic]

F 3 H 9

G 7 J 15

5. PSTV is a parallelogram, and V is the midpoint of [pic]

[pic]

Which is NOT necessarily true?

A TR ’ TV C [pic]||[pic]

B QS ’ SP D [pic] is a midsegment.

6. Which quadrilateral MUST be a parallelogram?

F [pic] H [pic]

G [pic] J [pic]

7. What is the sum of the measures of the interior angles of a regular 72-gon?

A 6480° C 12,960°

B 12,600° D 13,320°

8. In quadrilateral WXYZ, ∠W ” ∠Y. Which information would help to prove that WXYZ is a parallelogram?

F WY ’ XZ H WX ’ XY

G ∠X ” ∠W J ∠X ” ∠Z

9. The angles of a pentagon measure

x°, 2x°, 3x°, 4x°, and 5x°. What is

the measure of the smallest angle?

A 12° C 60°

B 36° D 108°

Polygons and Quadrilaterals

Section B Quiz

Choose the best answer.

1. Which MUST be a square?

A [pic] C [pic]

B [pic] D [pic]

2. Which is NOT necessarily a rhombus?

F [pic] H [pic]

G [pic] J [pic]

3. PQRS is a rectangle. Find ST.

[pic]

A 10 C 12.5

B 12 D 25

4. Quadrilateral RSTU is a parallelogram. What other information would allow you to prove that RSTU is a rectangle?

F Opposite angles are congruent.

G Opposite sides are congruent.

H The diagonals bisect the angles.

J The diagonals are congruent.

5. WXYZ is a rhombus. What is m∠XYZ?

[pic]

A 100° C 140°

B 120° D 160°

6. KLMN is a square and [pic].

[pic]

Which can be proved?

F (KPN ” (KQN

G [pic]

H KQ ’ PN

J KP ’ [pic]LN

7. A certain kite has exactly one acute angle, and it measures 16°. What is the maximum whole-number measure of the angle opposite that angle?

A 74° C 106°

B 90° D 164°

8. Three sides of a kite measure 8 inches, 10 inches, and 8 inches. What is the perimeter of the kite?

F 26 in. H 34 in.

G 28 in. J 36 in.

9. A trapezoid midsegment measures 6. One of the bases measures 10. What

is the measure of the other base?

A 2 C 14

B 8 D 16

Similarity

Section A Quiz

Choose the best answer.

1. Which is similar to this quadrilateral?

[pic]

A [pic] C [pic]

B [pic] D [pic]

2. Complete the similarity statement.

[pic]

ΔABC (   ?  

F ΔZYX H ΔXZY

G ΔYZX J ΔXYZ

3. Rob is making for his young son a replica armchair of one he uses. The ratio of the length of the arm of the old chair to that of the new chair is 3 : 2. The arm of the old chair is 9 inches long. How many inches long will the arm of the new chair be?

A 6 C [pic]

B 8 D 18

4. The dilation D: (x, y) ( (0.2x, 0.2y) has been applied to the polygon S(–5, 5), T(–5, 10), U(5, 15). What are the coordinates of the image points?

F S((–4.8, 5.2), T((–4.8, 10.2),

U((5.2, 15.2)

G S((–1, 1), T((–1, 2), U((1, 3)

H S((–5.2, 4.8), T((–5.2, 9.8), U((4.8, 14.8)

J S((–3, 7), T((–3, 12), U((7, 17)

5. Which transformation(s) can be used to show that polygon W(–2, 4), X(–2, 8),

Y(–6, 2), Z(–10, 4) is similar to polygon L(–3, 0), M(–3, 2), N(–5, –1), O(–7, 2)?

A first dilate: (x, y) → (0.5x, 0.5y) then translate: (x, y) → (x – 2, y – 2)

B translate: (x, y) → (x – 1, y – 4)

C first dilate: (x, y) → (2x, 2y) then translate: (x, y) → (x + 1, y + 8)

D translate: (x, y) → (x + 1, y + 4)

6. Which two triangles could you prove similar by AA (?

F [pic] H [pic]

G [pic] J

7. To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. What is AB to the nearest meter?

[pic]

A 10 C 15

B 12 D 18

Similarity

Section B Quiz

Choose the best answer.

1. For what value of JN is [pic] (( [pic]?

[pic]

A 5 C 20

B [pic] D 39.2

2. In the figure, [pic] (( [pic]. What is AE?

[pic]

F [pic] H [pic]

G 3 J 7

3. In the figure, KP ’ 50, KQ ’ 45,

PQ ’ 38. What is RQ?

[pic]

A 18 C 342

B 20 D 380

4. An architect uses the scale 2 inches :

5 feet to make a scale drawing for a new office building. The cafeteria will be 40 feet wide. How long should she make the segment to represent the cafeteria width?

F [pic]in. H 16 in.

G 4 in. J 100 in.

5. The scale on a map uses 3 centimeters to represent 4 kilometers. The distance between two towns on the map is

6 centimeters. How many kilometers

apart are the towns?

A 2 C 8

B 4.5 D 72

6. A rectangular classroom is 12 meters long and 8 meters wide. You want to make a scale drawing of the room using a scale of 1 centimeter : 4 meters. What will be the dimensions of your scale drawing?

F 48 cm by 32 cm

G 3 cm by 2 cm

H 8 cm by 4 cm

J 6 cm by 4 cm

7. The coordinates of ΔPMN are P(2, 10),

M(8, −6), and N(−4, 2). After a dilation, the image of P is (19, 95). What are the coordinates of the image of M?

A (76, −57) C (76, 380)

B (76, −6) D (76, −380)

8. Which method CANNOT be used to prove ΔABC ( ΔADE?

[pic]

F Use the Distance Formula to show

AB : AD ’ AC : AE, and ∠A ” ∠A. (SAS ()

G Use the Distance Formula to show

AB : AC : BC ’ AD : AE : DE.

(SSS ()

H ∠A ” ∠A by the Reflexive Property of Congruence. Measure to show

∠ABC ” ∠D. (AA ()

J Use the slope formula to show that the slopes of [pic] and [pic] are equal so [pic] (( [pic] and corresponding angles are congruent. (AA ()

Right Triangles and Trigonometry

Section A Quiz

Choose the best answer.

1. What is the length of the altitude to the hypotenuse in a right triangle if this altitude divides the hypotenuse into segments of lengths 8 millimeters and 18 millimeters?

A 12 mm C 26 mm

B 13 mm D 36 mm

Use the figure for Exercises 2 and 3.

[pic]

2. If XY ’ 10 and XW ’ 12, what is VY?

F 2 H 12

G 4.4 J 14.4

3. If XY ’ 9 and VW ’ 6, what is VX?

A 3 C 12

B 4 D 13

4. To estimate the height

of a flagpole, Marci, who

is 5 feet tall, stands so

that her lines of sight to

the top and bottom of

the pole form a 90°

angle. What is the

height of the pole to

the nearest foot?

F 9 ft H 25 ft

G 20 ft J 50 ft

5. One acute angle of a right triangle measures 28°. To the nearest tenth, what is the length of the side opposite that angle if the hypotenuse measures 16 meters?

A 7.5 m C 18.1 m

B 14.1 m D 34.1 m

Use the figure for Exercises 6 and 7.

[pic]

6. What is tan K?

F [pic] H [pic]

G [pic] J [pic]

7. To the nearest degree, what is m∠M?

A 2° C 62°

B 28° D 88°

8. A 24-foot ladder forms a 76° angle with the ground. The top of the ladder rests against a building. To the nearest inch, how high up the building does the ladder reach?

F 5 ft 10 in. H 18 ft 5 in.

G 18 ft 1 in. J 23 ft 3 in.

9. What is cos 30°?

A [pic] C [pic]

B [pic] D [pic]

10. To the nearest degree, what is the measure of the smallest angle of a right triangle whose legs measure 9 and 15?

F 31° H 53°

G 37° J 59°

11. To the nearest degree, what angle does a hill with a grade of 11% make with a horizontal line?

A 6° C 79°

B 11° D 84°

Right Triangles and Trigonometry

Section B Quiz

Choose the best answer.

1. An air traffic controller at an airport sights a plane at an angle of elevation of 28°. The pilot reports that the plane’s altitude is 4500 feet. To the nearest foot, what is the horizontal distance from the control tower to the plane?

A 2113 ft C 8463 ft

B 3190 ft D 9585 ft

2. The pilot of a helicopter sights a fire at an angle of depression of 11°. The helicopter’s altitude is 1700 feet. To the nearest foot, what is the horizontal distance from the helicopter to the fire?

F 324 ft H 1669 ft

G 330 ft J 8746 ft

3. The pilot of a helicopter hovers at an altitude of 1200 feet over a park. The angle of depression to the base of a statue is 17°. The angle of depression to the nearest park exit, in line with the statue, is 14°. To the nearest foot, what is the distance from the statue to the exit?

A 91 ft C 3925 ft

B 888 ft D 4813 ft

Use the figure for Exercises 4 and 5.

[pic]

4. Given that QR ’ 4.8, m∠R ’ 80°, and m∠P ’ 42°, what is PQ to the nearest tenth?

F 3.3 H 6.6

G 6.3 J 7.1

5. Given that ρPQR is acute, QR ’ 9.7, PR ’ 12.2, and m∠P ’ 43°, what is m∠Q to the nearest degree?

A 33° C 54°

B 40° D 59°

Use the figure for Exercises 6 and 7.

[pic]

6. Given that XZ ’ 9.8, XY ’ 21.2, and

m∠X ’ 108°, what is YZ to the nearest tenth?

F 26.0 H 12.6

G 20.4 J 9.9

7. If XY ’ 37.4, XZ ’ 17.1, and

YZ ’ 44.5, what is m∠Z to the

nearest degree?

A 1° C 55°

B 35° D 89°

8. What is the magnitude of the vector

(6, −1( to the nearest tenth?

F 5.9 H 25.0

G 6.1 J 49.0

9. The path of a ferryboat is given by the vector (3, 10(. Find the direction of the vector to the nearest degree.

A 15° C 73°

B 17° D 85°

10. A sailboat leaves a dock and heads

N 12° E for 8 miles. Then it heads

3 miles due south where it begins taking in water. In what direction should a rescue boat leave from the dock?

F N 19° E H N 31° E

G E 19° N J E 31° N

11. A plane flies 450 mi/h at a bearing of E 20° N. If a crosswind blows 40 mi/h northeast, what is the plane’s actual speed to the nearest mi/h?

A 415 mi/h C 435 mi/h

B 423 mi/h D 487 mi/h

Transformational Geometry

Section A Quiz

Choose the best answer.

1. What is the image of (−8, −1) when it is reflected across the line y ( x?

A (−1, −8) C (1, 8)

B [pic] D [pic]

2. Which of the following capital letters

is a reflection image of itself across a horizontal line?

F M H O

G N J P

3. The endpoints of [pic] are M(2, 5) and N(8, −1). Which shows the endpoints of the segment after it is translated along the vector (−2, 3(?

A M′(−4, −10), N′(24, −3)

B M′(−4, 15), N′(−16, −3)

C M′(0, 3), N′(11, 2)

D M′(0, 8), N′(6, 2)

4. The vertices of (PQR are P(10, −6),

Q(6, 2), and R(4, −1). The triangle is translated along a vector. Which vector places the image of the triangle entirely

in Quadrant II?

F 〈−6, 10〉 H 〈−11, 6〉

G 〈−10, 7〉 J 〈−12, 8〉

5. The point (90, 0) is rotated 150° about

the origin. What are the coordinates of

its image?

A (90, 150) C [pic]

B (90, 45) D [pic]

6. Which shows the image of after a

180° rotation about the endpoint of the ray?

F H

G J

Use the figure for Exercises 7–9.

The coordinates

of the vertices

are integers.

7. (JKL is rotated 90° about the origin

and then translated along the vector

〈−8, 5〉. What are the coordinates of

the final image of point L under this composition of transformations?

A (−7, 10) C (−9, 10)

B (−7, 0) D (−9, 0)

8. (JKL is translated along the vector

(1, −3〉 after it is reflected across the

x-axis. What are the coordinates of

the final image of point J under this composition of transformations?

F (6, −1) H (1, −6)

G (−6, 1) J (−1, 6)

9. (JKL is translated so that the image of vertex K is K′(4, −12). A composition

of reflections across the lines of which equations creates the same image?

A first y ’ (5, then y ’ −9

B first y ’ (5, then y ’ −1

C first y ’ −9, then y ’ −1

D first y ’ −1, then y ’ −9

10. The composition of two reflections

across two intersecting lines is

equivalent to which isometry?

F rotation H translation

G glide rotation J reflection

Transformational Geometry

Section B Quiz

Choose the best answer.

1. How many lines of symmetry does a regular hexagon have?

A 3 C 6

B 4 D 8

2. What is the order and angle of rotational symmetry of a regular octagon?

F 8; 45° H 4; 90°

G 16; 45° J 8; 90°

3. Which capital letter has exactly one line of symmetry?

A O C S

B P D T

4. Which shape CANNOT be used to make a regular tessellation?

F isosceles right triangle

G rhombus

H trapezoid

J regular pentagon

5. Which pair of regular polygons can be used to make a semiregular tessellation?

A [pic] C [pic]

B [pic] D [pic]

6. Which repeated transformation CANNOT be used alone to tessellate a square in a frieze pattern?

F 180° rotation about a vertex

G reflection

H translation

J glide reflection

7. Using only glide reflections, which of the following can tessellate the plane?

A regular octagon

B isosceles trapezoid

C circle segment

D circle

8. What is the scale factor of a dilation centered at the origin that maps the

point (12, −8) to the point (−7.2, 4.8)?

F [pic] H [pic]

G [pic] J [pic]

Use the figure for Exercises 9–11.

The coordinates

of the vertices

are integers.

9. ΔPQR is enlarged under a dilation centered at the origin with scale factor 3.5. What is the area of the image in square units?

A 14 units2 C 98 units2

B 49 units2 D 171.5 units2

10. What are the coordinates of point P after a dilation with a scale factor of −4?

F (−7, −2) H (12, −8)

G (1, 6) J (0.75, −0.5)

11. The graph of y ’ −2 is a line of

symmetry for ΔQRS. What are the coordinates of point S?

A (4, −6) C (−4, 2)

B (8, −2) D (0, 6)

Extending Perimeter, Circumference, and Area

Section A Quiz

Choose the best answer.

1. What is the height of a triangle whose base is 9.4 centimeters and whose area is 132.54 square centimeters?

A 7.05 cm C 28.2 cm

B 14.1 cm D 42.3 cm

2. The diagonals of a kite are 22 feet and 33 feet long. What is its area?

F 363 ft2 H 756.25 ft2

G 726 ft2 J 1452 ft2

3. A walkway along the diagonal of a square park is [pic] mile long. What is the area of the park?

A [pic] C [pic]

B [pic] D [pic]

4. Bryce has 220 feet of fencing that will enclose a rectangular corral. One side of the corral will be 48 feet long. What will be the area of the corral?

F 1488 ft2 H 2976 ft2

G 2304 ft2 J 8256 ft2

5. What is the circumference of a circle whose area is 121( square meters?

A 5.5 m C 22 m

B 5.5( m D 22( m

6. What is the diameter of a circle whose circumference is 16( centimeters?

F 4 cm H 16 cm

G 8 cm J 32 cm

7. What is the area of a regular hexagon whose perimeter is 24 feet?

A 24[pic] ft2 C 72[pic] ft2

B 48[pic] ft2 D 96[pic] ft2

8. What is the area of a regular octagon having an apothem of 6 meters and a side length of 5 meters?

F 15 m2 H 240 m2

G 120 m2 J 480 m2

9. What is the area of the figure to the nearest tenth?

[pic]

A 140.3 cm2 C 175.4 cm2

B 141.8 cm2 D 186.2 cm2

10. What is the area of the shaded region to the nearest tenth of a foot?

[pic]

F 140.1 ft2 H 447.9 ft2

G 294.0 ft2 J 601.9 ft2

For Exercises 11 and 12, choose the best estimate for the area of the shaded region.

11. Side lengths of grid

squares are 1 meter.

A 27.75 m2 C 35 m2

B 30.5 m2 D 55.5 m2

12. Side lengths of grid

squares are 1 inch.

F 25 in2 H 36 in2

G 29 in2 J 40 in2

Extending Perimeter, Circumference, and Area

Section B Quiz

Choose the best answer.

Use the figure for Exercises 1 and 2.

[pic]

1. What is the perimeter of the figure?

A 21 units C 26 units

B 24 units D 29 units

2. What is the area of the figure?

F 12 units2 H 17 units2

G 16 units2 J 24 units2

3. The area of a circle is 96 square inches. What is the area of a circle whose diameter is 1.5 times the diameter of

the circle?

A 48 in2 C 144 in2

B 64 in2 D 216 in2

4. A map has the scale of 2 centimeters ’ 1 kilometer. On a map, the area of a forest preserve is 3.8 square centimeters. What is the area of the actual forest preserve?

F 0.95 km2 H 7.6 km2

G 1.9 km2 J 15.2 km2

5. A pet store runs a monthly magazine ad that is 2 inches wide and 6 inches long and costs $366. The cost of each ad is based on its area. If the pet store manager decides to triple the width of the ad, how much will the new ad cost?

A $457.50 C $1098

B $549 D $3294

6. The perimeter of a rectangle is p units. If its length and width are tripled, what is the perimeter of the new rectangle?

F p + 12 units H p + 6 units

G 3p units J 9p units

7. What is the probability that the spinner lands on B or E?

[pic]

A 0.135 C 0.45

B 0.375 D 0.6

8. A stoplight has the following cycle: green for 90 seconds, yellow for 10 seconds, and red for 60 seconds. What is the probability that the light will be red for

a car approaching the stoplight?

F [pic] H [pic]

G [pic] J [pic]

9. The blue region of the Texas flag is

one-third the width, and the red and white stripes are each half the height. What is the probability that a butterfly landing on the flag lands on red?

[pic]

A [pic] C [pic]

B [pic] D [pic]

Spatial Reasoning

Section A Quiz

Choose the best answer.

1. Which identifies the figure?

[pic]

A rectangular pyramid

B rectangular prism

C cube

D square pyramid

2. What best describes the cross section shown on the cube?

[pic]

F square H trapezoid

G triangle J rectangle

3. The dimensions of a rectangular crate are 4 feet, 6 feet, and 8 feet. What is

the volume?

A 18 ft3 C 192 ft3

B 96 ft3 D 208 ft3

4. What is the volume of a prism with

a height of 4 feet and base area of

9 square feet?

F 36 ft3 H 120 ft3

G 36π ft3 J 120π ft3

5. What is the volume

of the cylinder?

A 75 m3

B 75π m3

C 281.25π m3

D 1125π m3

6. What is the volume of the pyramid?

[pic]

F 120 in3 H 240 in3

G 160 in3 J 480 in3

7. What is the volume of a cone with diameter 12 centimeters and height

4 centimeters?

A 48π cm3 C 192π cm3

B 72π cm3 D 288π cm3

8. What is the radius of a sphere whose volume is 36π cubic inches?

F 3 in. H 24 in.

G 3π in. J 24π in.

9. What is the surface area of a sphere whose great circle has an area of

30 square yards?

A 60 yd2 C 120 yd2

B 60π yd2 D 120π yd2

10. What is the volume of a sphere whose surface area is 36π square meters?

F 36 m3 H 72 m3

G 36π m3 J 72π m3

Circles

Section A Quiz

Choose the best answer.

Use the figure for Exercises 1–3.

[pic]

1. Which is a chord of circle P?

A line m C [pic]

B line n D [pic]

2. Which is a secant of circle P?

F line m H [pic]

G line n J [pic]

3. Which is a tangent of circle P?

A line m C [pic]

B line n D [pic]

4. The summit of Mt. McKinley is about 20,320 feet above sea level. Earth’s radius is about 3950 miles. To the nearest mile, what is the distance

from the summit to the horizon?

F 67 mi H 1633 mi

G 174 mi J 3950 mi

5. The central angle of a circle measures 97° and intercepts a minor arc. What is the measure of its major arc?

A 83° C 187°

B 97° D 263°

6. What is [pic]

F 70°

G 80°

H 100°

J 122°

7. What is XZ?

A 10

B 25

C 55

D 101.25

8. To the nearest

tenth, what is

MN?

F 24.2

G 27.0

H 48.4

J 54

9. The central angle of an arc measures 75°. The radius of the circle measures

3 meters. What is the area of the sector to the nearest tenth of a square meter?

A 0.6 m2 C 5.9 m2

B 3.9 m2 D 14.4 m2

10. An arc measures 50° in a circle with a radius of 8 centimeters. What is the area of the sector to the nearest tenth of a square centimeter?

F 7.0 cm2 H 57.6 cm2

G 27.9 cm2 J 174.5 cm2

11. The central angle of an arc measures 12°. The radius of its circle is 30 inches. What is the length of the arc to the nearest quarter inch?

A 1 in. C [pic]

B [pic] D [pic]

12. An arc measures 125° in a circle with a radius of 36 centimeters. What is the length of the arc to the nearest tenth?

F 11.3 cm H 78.5 cm

G 12.5 cm J 1562.5 cm

Circles

Section B Quiz

Choose the best answer.

1. What is

m(R?

A 45°

B 69°

C 79.5°

D 90°

2. An artist used this design to create a stained glass window. If m(M ( 48° and [pic]what is m(LKM?

[pic]

F 18° H 54°

G 36° J 72°

Use the figure for Exercises 3 and 4.

[pic]

3. What is the value of x?

A 52 C 86

B 68 D 104

4. What is the value of y?

F 55.5 H 111

G 107.5 J 215

5. Which equation is of a circle that has a center at (3, (2) and a radius of 9?

A (x ( 3)2 ( (y ( 2)2 ( 9

B (x ( 3)2 ( (y ( 2)2 ( 81

C (x ( 3)2 ( (y ( 2)2 ( 9

D (x ( 3)2 ( (y ( 2)2 ( 81

6. Six posts are evenly spaced along a circular wall encasing a fountain. Anna stands at point A, where she cannot see beyond the only two posts visible to her. What is m(A?

[pic]

F 100° H 125°

G 120° J 150°

7. What is the

value of x?

A 23 ft

B 28 ft

C 26.25 ft

D 42 ft

8. A plywood template for a kitchen breakfast bar is cut from a circle. ​[pic]

is the perpendicular bisector of [pic]

[pic]

What was the radius of the circle?

F 14 in. H 30 in.

G 25 in. J 31 in.

9. A radio antenna is kept perpendicular to the ground by three wires of equal length. The wires touch the ground at three points on a circle whose center is at the base of the antenna. If the wires touch the ground at (9, (19), ((21, (19), and (14, 16), what are the coordinates of the base of the antenna?

A ((6, 1) C ((4, 3)

B (6, (1) D (4, (3)

Answer Key Foundations for Geometry

Section Quiz: Lessons 1-1 Through 1-4

1. C 8. F

2. G 9. A

3. B 10. J

4. J 11. A

5. C 12. G

6. J 13. B

7. B

Section Quiz: Lessons 1-5 Through 1-7

1. D 5. D

2. H 6. H

3. C 7. B

4. F 8. G

Chapter Test Form A: Multiple Choice

1. C 11. D

2. B 12. A

3. D 13. A

4. B 14. C

5. C 15. B

6. B 16. B

7. A 17. A

8. D 18. A

9. A 19. A

10. A 20. A

Chapter Test Form B: Multiple Choice

1. C 11. B

2. F 12. G

3. D 13. A

4. G 14. H

5. D 15. B

6. J 16. J

7. C 17. C

8. J 18. F

9. D 19. B

10. J 20. J

Chapter Test Form C: Multiple Choice

1. D 11. B

2. G 12. G

3. D 13. D

4. F 14. F

5. C 15. A

6. F 16. H

7. D 17. C

8. G 18. G

9. B 19. A

10. H 20. F

Chapter Test Form A: Free Response

1. Possible answers: [pic] or line n

2. [pic] or [pic]

3. [pic]

4. point B

5. 28 units

6. 9 units

7. acute

8. 130°

9. Possible answers: ∠1 and ∠5, or

∠4 and ∠5

10. 61°

11. 43°

12. 28 cm

13. 24 in2

14. 18( ft

15. (−5, 6)

16. (14, 6)

17. [pic]

18. 5 cm

19. translation

20. A((1, 1), B((5, −1)

Answer Key Geometric Reasoning

Section Quiz: Lessons 2-1 Through 2-4

1. D 5. B

2. H 6. F

3. C 7. D

4. F

Section Quiz: Lessons 2-5 Through 2-7

1. B 4. J 7. B

2. J 5. A 8. H

3. C 6. H 9. C

Chapter Test Form A: Multiple Choice

1. B 6. B 11. C

2. C 7. C 12. B

3. A 8. B 13. A

4. B 9. D 14. A

5. A 10. B

Chapter Test Form B: Multiple Choice

1. A 8. H

2. H 9. A

3. C 10. J

4. H 11. C

5. B 12. H

6. J 13. C

7. A 14. F

Chapter Test Form C: Multiple Choice

1. C 8. G

2. H 9. D

3. A 10. G

4. J 11. D

5. C 12. H

6. H 13. D

7. B 14. G

Chapter Test Form A: Free Response

1. 17

2. Possible answer: receive

3. Hypothesis: It is raining.

Conclusion: There are clouds in the sky.

4. True

5. If two angles have the same measure, then they are congruent.

6. valid

7. valid

8. A rectangle is a square if and only if it

has four congruent sides.

9. x ( 5 ( 12 Given equation

x ( 5 − 5 ( 12 − 5 Subtr. Prop. of (

x ( 7 Simplify.

10. ∠A

11. theorem

12. Def. of ( [pic]

13. m∠A ( m∠B ( 180°

14. False

Chapter Test Form B: Free Response

1. 21

2. Possible answer: 9 − 3 ( 6

3. Hypothesis: An angle has a measure

less than 90°.

Conclusion: The angle is acute.

4. False

5. If the sum of two whole numbers is not even, then both addends are not even.

6. valid

7. not valid

8. A rectangle is a square if and only if it has four congruent sides.

9. 5m − 3 ( 22 Given equation

5m − 3 ( 3 ( 22 ( 3 Add. Prop. of (

5m ( 25 Simplify.

[pic] Div. Prop. of (

m ( 5 Simplify.

Answer Key Parallel and Perpendicular Lines

Section Quiz: Lessons 3-1 Through 3-4

1. D 5. A

2. H 6. G

3. B 7. C

4. G 8. J

Section Quiz: Lessons 3-5 Through 3-6

1. B 6. G

2. H 7. A

3. D 8. F

4. J 9. A

5. C 10. H

Chapter Test Form A: Multiple Choice

1. B 11. A

2. A 12. A

3. A 13. B

4. A 14. A

5. B 15. A

6. B 16. D

7. B 17. A

8. C 18. A

9. B 19. B

10. B 20. C

Chapter Test Form B: Multiple Choice

1. C 11. B

2. J 12. H

3. B 13. A

4. G 14. H

5. A 15. B

6. G 16. F

7. A 17. D

8. H 18. J

9. A 19. A

10. F 20. J

Chapter Test Form C: Multiple Choice

1. A 11. A

2. F 12. J

3. C 13. C

4. G 14. J

5. A 15. D

6. G 16. G

7. C 17. B

8. H 18. G

9. A 19. D

10. J 20. H

Chapter Test Form A: Free Response

1. Sample answer: [pic] and [pic]

2. False

3. eight

4. alternate interior angles

5. four

6. congruent

7. 135°

8. True

9. Conv. of the Alt. Ext. [pic] Thm.

10. one

11. [pic]

12. x ( 3 ( 28; x ( 25

13. perpendicular

14. rise

15. 2

16. parallel

17. True

18. y ( 3x − 5

19. [pic]

20. parallel

Answer Key Triangle Congruence

Section Quiz: Lessons 4-1 Through 4-4

1. C 7. A

2. J 8. G

3. D 9. C

4. J 10. G

5. D 11. D

6. J 12. H

Section Quiz: Lessons 4-5 Through 4-9

1. B 6. G

2. J 7. C

3. D 8. H

4. J 9. D

5. D 10. H

Chapter Test Form A: Multiple Choice

1. A 9. D

2. C 10. C

3. A 11. B

4. C 12. A

5. B 13. B

6. A 14. B

7. B 15. B

8. A 16. D

Chapter Test Form B: Multiple Choice

1. C 7. C 13. D

2. H 8. G 14. F

3. B 9. B 15. A

4. J 10. G 16. F

5. C 11. A 17. B

6. J 12. J 18. H

Chapter Test Form C: Multiple Choice

1. D 9. D

2. F 10. J

3. C 11. B

4. H 12. H

5. A 13. A

6. G 14. F

7. D 15. A

8. J 16. J

Chapter Test Form A: Free Response

1. M9(2,2)

2. yes

3. acute

4. isosceles

5. 60°

6. 45°

7. 35

8. 5

9. corresponding

10. 6

12. True

13. [pic]

14. True

15. False

16. 62

17. Isosceles Triangle Theorem

18. True

Chapter Test Form B: Free Response

1. This is a translation 4 units right and 6 units down.

2. No; ΔABC is mapped to ΔDEF by a dilation with a scale factor that doesn't equal 1: (x, y) ( (2.5x, 2.5y)

3. right

4. equilateral

5. 63°

6. 52°

7. 30

8. m∠U ( 120°; UV ( 17

9. ∠1 ( ∠2; Third [pic] Thm.

10. 8

11. SAS

12. ∠ADB ( ∠DAC

13. HL

14. Possible answer: A(−2, 0), B(0, 4),

C(2, 0), D(0,0)

15.Possible answer: ΔABD is a right triangle

with base AD and height BD. ΔCBD is a right triangle with base CD and height BD.

Answer Key Properties and Attributes of Triangles

Section Quiz: Lessons 5-1 Through 5-4

1. C 5. B

2. J 6. J

3. A 7. A

4. H 8. G

Section Quiz: Lessons 5-5 Through 5-8

1. D 7. C

2. G 8. J

3. C 9. A

4. J 10. G

5. A 11. B

6. F

Chapter Test Form A: Multiple Choice

1. C 10. C

2. B 11. D

3. B 12. D

4. A 13. B

5. C 14. A

6. B 15. A

7. A 16. A

8. B 17. C

9. A 18. D

Chapter Test Form B: Multiple Choice

1. B 10. G

2. H 11. D

3. C 12. J

4. G 13. A

5. A 14. G

6. F 15. C

7. A 16. J

8. J 17. C

9. C 18. G

Chapter Test Form C: Multiple Choice

1. B 10. G

2. F 11. B

3. B 12. J

4. F 13. D

5. A 14. H

6. G 15. A

7. C 16. H

8. J 17. D

9. C 18. H

Chapter Test Form A: Free Response

1. 12.5

2. (2, 6)

3. 17.25

4. QO ( 3.75, RP ( 3.4, and PT ( 4.5

5. m∠XHG ( 39°; the distance from

X to [pic]

6. MW ( 10

7. altitudes

8. 21.25

9. 45°

10. True

11. True

12. [pic]

13. FD ( GJ

14. 10

15. True

16. right

17. [pic]

18. [pic]

Chapter Test Form B: Free Response

1. 32

2. [pic]

3. 33°

4. XT ( 16, VU ( 30, and ZV ( 20

5. m∠HJX ( 18°; the distance from x

to [pic]

6. LZ ( 18.3; MW ( 14.4

7. (−3.5, 5)

8. 24 units

9. 145°

10. either m∠P ( m∠Q or m∠P ( m∠Q

Answer Key Polygons and Quadrilaterals

Section Quiz: Lessons 6-1 Through 6-3

1. D 6. F

2. H 7. B

3. D 8. J

4. H 9. B

5. A

Section Quiz: Lessons 6-4 Through 6-6

1. A 6. G

2. J 7. D

3. A 8. J

4. J 9. A

5. A

Chapter Test Form A: Multiple Choice

1. D 9. C

2. C 10. A

3. A 11. A

4. D 12. B

5. A 13. B

6. A 14. A

7. B 15. A

8. A 16. A

Chapter Test Form B: Multiple Choice

1. C 9. C

2. G 10. J

3. A 11. D

4. F 12. G

5. C 13. D

6. H 14. H

7. B 15. B

8. J 16. H

Chapter Test Form C: Multiple Choice

1. C 9. D

2. G 10. H

3. D 11. B

4. F 12. F

5. D 13. B

6. G 14. J

7. C 15. A

8. J 16. F

Chapter Test Form A: Free Response

1. True

2. 540°

3. 90°

4. False

5. 11

6. 66°

7. True

8. Find JM and KL.

JM ( 5x − 1 and KL ( 3x ( 5 Given

JM ( 5(3) − 1 ( 14 Subst. and simplify.

KL ( 3(3) ( 5 ( 14 Subst. and simplify.

Since JM ( KL and [pic] JKLM is a parallelogram by Theorem 6-3-1.

9. True

10. 25

11. 56°

12. True

13. valid

14. 65°

15. 104°

16. 72

Chapter Test Form B: Free Response

1. irregular hexagon

2. 135°

3. 120°

4. A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides.

5. AB ( 30; BX ( 25

6. 70°

7. True

Answer Key Similarity

Section Quiz: Lessons 7-1 Through 7-3

1. B 5. A

2. F 6. F

3. A 7. C

4. G

Section Quiz: Lessons 7-4 Through 7-6

1. C 5. C

2. H 6. G

3. A 7. A

4. H 8. H

Chapter Test Form A: Multiple Choice

1. A 8. B

2. C 9. B

3. D 10. B

4. B 11. A

5. B 12. D

6. A 13. C

7. A 14. B

Chapter Test Form B: Multiple Choice

1. B 8. G

2. F 9. C

3. C 10. G

4. H 11. D

5. A 12. J

6. G 13. A

7. A 14. J

Chapter Test Form C: Multiple Choice

1. D 8. G

2. H 9. B

3. D 10. J

4. F 11. B

5. G 12. G

6. H 13. C

7. C 14. J

Chapter Test Form A: Free Response

1. Yes; [pic] ΔABC [pic] ΔFDE

2. 7 in.

3. 2.4 cm

4. "a transformation that maps (x, y) to

(kx, ky), where k ( 0(

5. A9(12, 12), B9(3, 3), C9(18, 24)

6. Possible answer: dilation: (x, y) (

(2x, 2y) and then translation: (x, y)

( (x 1 4, y 1 4)

7. AA [pic]

8. 50

9. True

10. 25

11. 12 ft

12. 39 ft

13. V(6, 0); 2

14. AB ( 3, AD ( 6, AC ( 4, and AE ( 8.

[pic] so corresponding sides are proportional.∠A ( ∠A by the Reflexive Property. So ΔABC [pic] ΔADE by SAS [pic].

Chapter Test Form B: Free Response

1. Yes; [pic] ΔABC [pic] ΔFED

2. [pic] ft

3. 6.4 m

4. Possible answer: M: (x, y) ( (ax, by) where a and b are constants and a ( b

5. "dilation with center (0, 0) and scale factor [pic]”

6. Possible answer: first translate: (x, y) ( (x + 4, y + 5) and then dilate: (x, y) ( (0.5x, 0.5y)

7. ∠GJH ( ∠LJK by Vertical Angles Theorem. From the figure, we know that ∠H ( ∠K. So ΔGJH [pic] ΔLJK by AA [pic]

Answer Key Right Triangles and Trigonometry

Section Quiz: Lessons 8-1 Through 8-3

1. A 5. A 9. B

2. G 6. G 10. F

3. C 7. C 11. A

4. H 8. J

Section Quiz: Lessons 8-4 Through 8-6

1. C 5. D 9. C

2. J 6. F 10. F

3. B 7. C 11. D

4. J 8. G

Chapter Test Form A: Multiple Choice

1. C 6. B 11. A

2. B 7. A 12. A

3. D 8. A 13. C

4. C 9. B 14. A

5. B 10. A 15. A

Chapter Test Form B: Multiple Choice

1. D 6. G 11. B

2. G 7. A 12. J

3. C 8. F 13. C

4. H 9. B 14. G

5. C 10. H 15. B

Chapter Test Form C: Multiple Choice

1. C 6. G 11. C

2. G 7. C 12. F

3. B 8. F 13. B

4. J 9. B 14. J

5. C 10. H 15. C

Chapter Test Form A: Free Response

1. 4 9. elevation

2. 20 m 10. 53 ft

3. [pic] 11. Law of Cosines

4. 0.6 12. 11

5. 63 13. 5

6. 13 ft 14. 53°

7. ∠A 15. 10; 53°

8. 4°

Chapter Test Form B: Free Response

1. 25 9. 1991 ft

2. [pic] 10. 4744 ft

3. 0.55 11. 17 cm

4. [pic] 12. 3.1

5. 65 13. [pic], or about 6.4

6. 48 ft 14. 27°

7. 53° 15. 325.0 mi/h;

8. 38° N 58° E

Chapter Test Form C: Free Response

1. x ( 24, y ( 12, [pic]

2. 76.5 ft

3. 0.86

4.

| |30° |45° |60° |

|sin |[pic] |[pic] |[pic] |

|cos |[pic] |[pic] |[pic] |

|tan |[pic] |1 |[pic] |

5. perimeter ( 21.1 cm; area ( 18.2 cm2

6. 18

7. 43°

8. 66°

9. 4 min

10. 1675 ft

Answer Key Transformational Geometry

Section Quiz: Lessons 9-1 Through 9-4

1. A 6. G

2. H 7. A

3. D 8. H

4. J 9. D

5. C 10. F

Section Quiz: Lessons 9-5 Through 9-7

1. C 7. B

2. F 8. G

3. D 9. D

4. J 10. H

5. B 11. A

6. F

Chapter Test Form A: Multiple Choice

1. A 9. B

2. D 10. D

3. A 11. B

4. C 12. A

5. B 13. A

6. A 14. B

7. D 15. B

8. A

Chapter Test Form B: Multiple Choice

1. C 9. A

2. J 10. H

3. B 11. B

4. H 12. J

5. C 13. C

6. G 14. F

7. A 15. B

8. G

Chapter Test Form C: Multiple Choice

1. D 9. A

2. J 10. F

3. B 11. A

4. G 12. J

5. A 13. C

6. H 14. G

7. C 15. B

8. G

Chapter Test Form A: Free Response

1. False

2. Q((2, 1)

3. True

4. [pic]

5. True

6. [pic]

7. [pic]

8. True

9. translation

10. True; 8

Answer Key Extending Perimeter, Circumference, and Area

Section Quiz: Lessons 10-1 Through 10-3

1. C 7. A

2. F 8. G

3. A 9. D

4. H 10. F

5. D 11. A

6. H 12. G

Section Quiz: Lessons 10-4 Through 10-6

1. B 6. G

2. H 7. B

3. D 8. G

4. F 9. B

5. C

Chapter Test Form A: Multiple Choice

1. A 10. A

2. B 11. B

3. C 12. D

4. B 13. C

5. C 14. A

6. B 15. A

7. B 16. A

8. C 17. B

9. C 18. B

Chapter Test Form B: Multiple Choice

1. A 10. G

2. F 11. C

3. D 12. G

4. G 13. D

5. B 14. G

6. G 15. C

7. B 16. G

8. F 17. B

9. B 18. H

Chapter Test Form C: Multiple Choice

1. C 10. F

2. H 11. D

3. B 12. H

4. H 13. B

5. B 14. G

6. H 15. D

7. C 16. H

8. H 17. B

9. B 18. G

Chapter Test Form A: Free Response

1. 54 cm2

2. 66 cm2

3. 108 in2

4. 144 cm2

5. 40 in2

6. 49 in2

7. 6( cm

8. 16( cm2

9. 61.9 cm2

10. 432 cm2

11. about 3 in2

12. 10 units

13. 9 units2

14. 12 units2

15. The circumference is multiplied by 2.

16. Possible answers: double the width; double the length.

17. [pic]

18. [pic] or 0.5

Chapter Test Form B: Free Response

1. 60 cm2

2. 264 cm2

3. 216 cm2

4. 7 ft

5. 168 cm2

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