Geometry Review for Fall Final - Georgetown ISD



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Geometry Fall Semester Exam Review

Part I : True/ False

State whether the following is true or false. For every statement that is false, write or draw a counterexample showing why the statement is false.

1. Complementary angles are always adjacent.

2. If a triangle has two congruent angles, then it is an isosceles triangle.

3. If two lines are skew, they must intersect.

4. Diagonals of a rectangle are congruent.

5. A square is both a rhombus and rectangle.

6. The sum of the exterior angles to any polygon is 360 degrees.

7. An eighty degree angle and a twenty degree angle are complementary.

8. If a polygon has only one pair of parallel sides, it is a parallelogram.

9. The non-vertex angles of a kite are congruent.

10. Two triangles can be proven congruent by the Angle-Angle-Angle congruence conjecture.

Multiple Choice:

11. If two parallel lines are intersected by a transversal, then alternate exterior angles are _____.

A. complements B. supplements C. congruent D. adjacent

12. A segment from a vertex of a triangle perpendicular to the opposite side is a(n) _____.

A. median B. perpendicular bisector C. angle bisector D. altitude

13. A segment joining the midpoints of two sides of a triangle is a ______.

A. median B. midsegment C. altitude D. bisector

14. A parallelogram with congruent consecutive sides is a _____.

A. square B. rectangle C. rhombus D. triangle

Converse:

15. Statement: If two lines are perpendicular, then they form right angles.

Write the converse of this statement.

Part II: Finding missing angle measures

Work each problem carefully and answer the question.

16. An angle has a measure x. A complement of the angle has the measure 2x - 18. Find the angle.

17. The lengths of the legs of an isosceles triangle are 2x and 3x – 9. Find x.

18. An angle with measure x is bisected. One of the angles formed has measure x-10. Find the angle.

19. Show work to find the value of x. 20. Find x.

21. Find y. 22. Find x.

23. Find x. 24. Given[pic]

solve for x.

25. Using the figure on the right, find[pic] if [pic] and [pic].

Use the figure at the right for 26—28.

26. Find [pic] if [pic] bisects [pic],

[pic], and [pic].

27. Find [pic] if [pic] and [pic].

28. Find the value of [pic] if [pic],

[pic], and [pic].

Use the figure at the right for 29—31.

29. Name two right angles.

30. Name two congruent angles that are not right angles.

31. Name the obtuse angle.

32. Find the value of [pic] in the figure at the right.

33. M is in the interior of [pic]. [pic]

34. Find the value of [pic].

35. Find [pic] 36. Given [pic]

Find [pic]

37. [pic] are supplementary, with [pic] Find [pic]

Use the figure to the right for 38 and 39. [pic]

38. Find [pic].

39. Find [pic].

In the figure below, l // m, [pic]//[pic], [pic] bisects [pic], and [pic].

Find the measure of each angle.

40. m[pic] 40. _______________

41. [pic] 41. _______________

42. [pic] 42. _______________

43. [pic] 43. _______________

44. Find the measure of each lettered angle.

a = _______ f = _______

b = _______ g = _______

c = _______ m = _______

d = _______ p = _______

e = _______

Part III: Congruent Triangles

For problems 45-50, name the congruent triangles and state the conjecture (SSS, SAS, ASA, SAA) that supports the congruence statement. If you cannot show the triangles to be congruent, write “cannot be determined.”

45. 46. 47.

(ABC ( ( _____ (ABC ( ( _____ (ABC ( ( _____

by _______ by _______ by _______

48. 49. 50.

(ABC ( ( _____ (ABC ( ( _____ (ABC ( ( _____

by _______ by _______ by _______

(C ( ( _____ by ________ ED ( ____ by _______ AC ( ____ by _______

51. Given (DCE ( (BAE. Name the angle corresponding to [pic].

52. If (ART ( (GYM then AT = __________________.

53. What does CPCTC mean? _____________________________________________________

54. (ABC ( (TRQ. Name the 6 pairs of corresponding congruent parts.

1. ___________________ 4. _____________________

2. ___________________ 5. _____________________

3. ___________________ 6. _____________________

Part IV: Midpoint

55. If H is the midpoint of [pic] and TH = 28, then TE = __________.

56. Find the midpoint of a line segment with endpoints K (11, -8) and J (-9, 3).

57. The midpoint of [pic] is (2, 4). If the coordinates of B are (8, 6), what are the coordinates of A?

Part V: Quadrilaterals:

In problems 41-46, draw and label the figure as described. Then, find the solution.

58. ABCD is a parallelogram. If AB = 2x + 3 and DC = 3x – 5, find AB.

59. ABCD is a parallelogram. If m(ABC = 5x + 5and m(BCD = 3x + 15, find m(BAD.

60. ABCD is a rectangle with diagonals [pic] and [pic] intersecting at point E. If AE = 8, find DB.

61. ABCD is a rectangle with diagonals [pic] and [pic] intersecting at point E. m(ACB = 53.

Find m(AEB.

62. ABCD is a rhombus with diagonals [pic] and [pic] intersecting at point E. m(ADE = 40. Find m(EAD.

63. ABCD is a rhombus with diagonals [pic] and [pic]. m(CDA = 86. Find m(CDB.

63. What is the most accurate name for figure ABCD,

with vertices A(4, 6) B(8, 7) C(7, 3) D(3, 2)?

64. Refer to kite ABCD to find the following angles.

a. [pic] ______

b. [pic] ______

c. [pic] ______

65. Refer to isosceles trapezoid [pic] to find the missing measurements.

a. If DN = 18, find [pic].

b. If CN = 13, find DM.

c. If [pic], find [pic].

d. If [pic] and [pic], find [pic].

e. If the perimeter of CDMN is 266 cm, [pic]cm, and [pic]cm, find [pic].

Part VI: Lines

Use the figure below to answer questions 1-3. [pic] is a right triangle.

[pic]

1. Find the equation of the line containing [pic].

2. Find the equation of the line containing [pic].

3. Find the equation of the line containing [pic].

For questions 4-6, determine whether the equations of the lines given are parallel, perpendicular, or neither.

4. [pic] and [pic]

5. [pic] and [pic]

6. [pic] and [pic]

Distance Formula

7. Given points [pic] and [pic], find [pic].

8. Given [pic] with coordinates [pic], [pic], and [pic].

a. Find [pic]

b. Find [pic]

c. Find [pic]

d. Determine whether [pic] is scalene, isosceles, or equilateral.

Midpoint Formula

9. X is the midpoint of[pic]. The coordinates of S are (5, -8) and the coordinates of T are (7, -12). Find the coordinates of X.

10. The midpoint M of [pic] has coordinates, (5, 17). If the coordinates of B are (-1, 9), what are the coordinates of A?

Part VII: Logic

Determine if each each statement is true or false. If the statement is false provide a counterexample

11. All parallelograms are quadrilaterals

12. All squares are rhombi

13. All quadrilaterals are parallelograms

14. All rectangles are squares

15. Given: Two angles are vertical

The measure of one angle is twice the measure of the other angle

Conclusion: The measures of the angles are 40 and 80

The conclusion is:

A. Contradicted by the second statement

B. Verified by the second statement

C. Invalidates itself because vertical angles cannot be congruent

D. Verifies itself because 80 is twice 40

16. Which figure can serve as a counter example to the conjecture below?

If the diagonals of a quadrilateral are congruent then it is a parallelogram.

A. B. C. D.

Part VIII: Constructions

For Exercises 1-6, match each geometric construction with one of the figures below.

a. Construction of a perpendicular bisector of a segment

b. Construction of parallel lines

c. Construction of an angle bisector

d. Construction of a midsegment of a triangle

e. Construction of a an altitude

f. Construction of a midsegment of a trapezoid

-----------------------

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

1

2

A

C

B

D

1

2

M

N

K

L

25o

39o

116o

65o

25o

(2y+25)o

(3y+13)o

49o

34o

(4x-3)o

(3x+56)o

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

A

C

D

B

38o

2x-5

x+3

1

2

3

4

5

6

7

8

9

10

11

14

13

12

15

A

B

C

D

E

l

m

a

b

c

d

e

f

g

m

p

l

k

l // k

C

D

E

A

B

B

A

A

C

D

D

B

C

B

A

A

A

E

E

C

B

D

C

D

B

D

C

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

A

B

C

D

x

y

z

50o

80o

N

D

C

M

C

B

A

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