Montgomery Township School District / Montgomery …
Multiple Choice
Refer to the figure below for questions 1 and 2.
1. Points E,G. and F
A. determine a plane
B. are collinear
C. are contained in only plane JKH
D. are noncoplanar points
2. The line that contains F and K
A. intersects plane EGI but not plane JKH
B. intersects plane JKH but not plane EGI
C. does not intersect either plane
D. intersects both planes
3. What is the measure of [pic] if D is between A and B, AD=7 and DB=12.
A. 12 B. 5 C. 19 D. 10
4. If [pic] and [pic] form a linear pair and [pic] is acute, then [pic]is
a. acute b. obtuse c. right
5. If [pic] bisects [pic] and [pic], find [pic].
a. [pic] b. [pic] c. [pic] d. [pic]
6. The endpoints of [pic] are[pic] and [pic]. Find the midpoint [pic]of [pic].
A. [pic] C. [pic]
B. [pic] D. [pic]
7. [pic]has a length of 4.5 units. If [pic]has endpoints [pic]and [pic], how much longer than [pic]is [pic]?
A. 0.5 units C. 2 units
B. 2.5 units D. [pic]is longer
8. Name the acute angles in the given figure.
A. [pic] and [pic]
B. [pic] and [pic]
C. [pic]and [pic]
D. [pic] and [pic]
9. If the measure of [pic] is [pic], find the measure of [pic].
A. [pic] B. [pic] C. [pic] D. [pic]
10. [pic] is [pic]greater than [pic]. If [pic] and [pic] are supplementary, find [pic] and [pic].
A. [pic]
B. [pic]
C. [pic]
D. [pic]
Open Ended
Use the diagram to decide whether the given statement is true or false.
1. Points H, I, and J are coplanar.
2. and are opposite rays.
3. All points on and are coplanar.
4. The intersection of and plane JKH is
5. The intersection of , and is point G
6. The intersection of plane EGH and plane JGI is point G..
7. a. Find the distance between [pic]and [pic].
b. Find the midpoint of [pic]and [pic].
8. If [pic], find the value of x.
9. A segment with an endpoint at N(9,3) has its midpoint at M(7,4). Find the coordinates of the other endpoint.
Answers
1. _________________
2. _________________
3. ________________
4. ________________
5. ________________
6. ________________
7. a.________________
b.________________
8. ________________
9. ________________
10. ________________
11. ________________
10. The measure of an angle is half the measure of its supplement. Find the measure of the angle.
11,Find the value of y in the drawing below.
Multiple Choice
1. If 3 points lie in a plane, what must be true about the three points?
A. They must be collinear.
B. None of the points lie in any other plane.
C. None of the points lie on the same line.
D. None of these.
2. What is the converse of the given statement?
GIVEN: If [pic], then [pic]is a right angle.
A. If [pic], then [pic]is not a right angle.
B. If [pic], then [pic]is not a right angle.
C. If [pic] is not a right angle, then [pic].
D. If [pic]is a right angle, then [pic].
3. Which statement’s inverse is true?
A. If two lines intersect to form a right angle, then they are perpendicular lines.
B. If [pic]is less than [pic], then [pic]is acute.
C. If point K is the midpoint of [pic], then points J, K and L are collinear.
D. If two rays are opposite rays, then they have a common endpoint.
4. If all sides of a polygon are congruent, then the polygon is equilateral. All sides of polygon A are 5 inches. Using the Law of Detachment, which conclusion can be made?
A. Polygon A is congruent.
B. Polygon A is equilateral.
C. All polygon sides are 5 inches.
D. All polygons are equilateral.
5. If point B bisects [pic], then [pic]. If point B is the midpoint of [pic], then point B bisects [pic]. Using the Law of Syllogism, which conclusion can be drawn?
A. If point B is the midpoint of [pic], then [pic].
B. If [pic], then point B bisects [pic].
C. If [pic], then point B is the midpoint of [pic].
D. Points A, B and C are collinear.
6. Identify the property of equality that justifies the statement If AB=CD, then CD=AB.
a. Transitive b. Substitution
c. Symmetric d. Reflexive
7. The Reflexive Property of Equality states For every number a, ___________.
a. a = b b. a = a c. a = 0 d. b = a
Open Ended
1. The Law of Detachment states that if [pic] is true, then _____________ is true.
2. The Law of Syllogism states that if [pic] and [pic] are true, then _________________ is true.
In exercises 3-8, complete each statement given that [pic]
3. If [pic], then [pic].
4. If [pic], then [pic]________.
5. If [pic], then [pic]_________.
6. If [pic], then [pic]= ________.
7. If [pic], then [pic]=__________.
8. If [pic], then [pic]= _________.
Determine if a valid conclusion can be reached from the two true statements. If it can, state it and the law of logic that is used. If a valid conclusion does not follow, write no conclusion.
9. (1) If you can drive a car, then you have a driver’s licesnse. (2) Fran can drive a car.
10. (1) If [pic], then[pic].
(2) If [pic], then [pic].
11. (1) All vertical angles are congruent.
(2) [pic] and [pic]are congruent.
Answers
1. _________________
2. _________________
3. ________________
4. ________________
5. ________________
6. ________________
7. ________________
8. ________________
9. ________________
10. ________________
11. ________________
Multiple Choice
Use the drawing below for numbers 1-4.
1. Identify the special angle pair name for [pic] and [pic].
A. vertical
B. alternate interior
C. corresponding
D. consecutive exterior
2. Given [pic] and [pic] find [pic].
A. [pic] B. [pic]
C. [pic] D. [pic]
3. Given [pic] and [pic] and [pic] find the value of [pic].
A. 9 B. 42 C. 5 D. 36
4. Given[pic] and [pic], find the value of x so that [pic].
A. [pic] B. [pic] C. [pic] D. [pic]
5. Describe the slope of a line through [pic] and B(4,-3).
A. positive C. zero
B. negative D. undefined
6. Write an equation of the line with slope 2 and y-intercept 5.
A. [pic] C. [pic]
B. [pic] D. [pic]
7. Based on the diagram, which theorem would you use to support the statement [pic][pic]?
A. Alternate interior angles theorem
B. Alternate exterior angles theorem
C. Consecutive interior angles theorem
D. Parallel lines theorem
8. Find the value of [pic]and [pic].
A. [pic] C. [pic]
B. [pic] D. [pic]
9.
Find the value of x.
A. 36 B. 45
C. 60 D. 72
10. Find the slope of a line through [pic]and [pic]
A. 2 C. [pic]
B. –2 D. [pic]
Open Ended
Complete each of the following with
[pic]or no parallel lines.
1. If [pic], then _______________.
2. If [pic], then _______________.
3. If [pic], then ______________.
4. If [pic]is supplementary to [pic], then ______________.
5. If [pic] and [pic], then ____________.
6. If [pic], then ___________.
7. Find the value of [pic]so that [pic].
a.
b.
Answers
1. _________________
2. ________________
3. ________________
4. ________________
5. ________________
6. ________________
7. a.________________
b.________________
What 2 lines if any are parallel if the given information is true (if none, write no lines parallel)?
1. [pic]
2. [pic]
3. [pic]
4. [pic]
5. [pic]
6. [pic]
7. [pic]
8. [pic]and [pic]are supplementary
9. [pic] and [pic]are supplementary
10. [pic] and [pic] are complementary and [pic].
11. Tell whether a line whose slope is 0 is horizontal, vertical, or neither.
12. Write an equation in slope intercept form of the line parallel to the line passing through the given points.
a. G(-8,2), H(-3,12)
b. J(3,2), K(-1,-1)
c. M(-5,1), N(0,-7)
13. Write an equation of the line in standard form of the line perpendicular to the line passing through the given points.
a. P(6,1), Q(8,0)
b. R(3,-3), S(-1,5)
Answers
1. _________________
2. ________________
3. ________________
4. ________________
5. ________________
6. ________________
7. ________________
8. ________________
9. ________________
10. ________________
11. ________________
12. a.________________
b.________________
c.________________
13. a. ________________
b. ________________
c. ________________
Multiple Choice
In exercises 1-3 use the following drawing.
1. What is the value of [pic]?
A. 3 D.6
B. 4 E. 7
C. 5
2. What is the measure of the largest angle?
A. [pic] D. [pic]
B. [pic] E. [pic]
C. [pic]
3. What is the best classification for the triangle?
A. Right D. Equilateral
B. Acute E. Equiangular
C. Obtuse
4. Which congruence statement is correct for the triangles shown?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
E. [pic]
5. The sum of the measures of the interior angles of a triangle is _________.
A. [pic] C. [pic]
B. [pic] D. [pic]
6. Given [pic], use the Hypotenuse-Leg Congruence Theorem to find [pic].
A. 30 C. 60
B. 45 D. 90
7. If [pic] is isosceles and [pic], which statement must be true?
a. [pic] b. [pic]
c. [pic] d. [pic]
8. In [pic], the measure of each angle is 60[pic], [pic] and [pic]. Find the length of [pic].
a. 4 b. 5 c. 15 d. 16
9. Given [pic], [pic], [pic] and [pic], find the value of x.
a. 28 b. 13 c. 9 d. 7
10. Given [pic], [pic], [pic] and [pic], find the value of x.
a. 7 b. 14 c. 27 d. 84
11. Which of the following is not a postulate used to prove the congruence of triangles?
A. SSS B. AAS C. ASA D. AAA
12. In [pic], what angle is opposite [pic]?
a. [pic] b. [pic] c. [pic] d. [pic]
13. In isosceles triangle [pic], [pic] is the vertex angle. If [pic] and [pic], find the measure of [pic].
A. 6 B. 12 C. 44 D. 92
14. Classify the triangle ABC with vertices
A(-2,-1), B(6,1) and C(3,4).
A. right B. obtuse C. acute
D. equiangular
15. The measure of a base angle of an isosceles triangle is 25[pic]. What is the measure of the vertex angle?
A. 25[pic] B. 50[pic] C. 110[pic] D. 130[pic]
Open Ended
[pic]
Answers
1. _________________
2. _________________
3. ________________
4. ________________
5. ________________
6. ________________
7. ________________
8. ________________
9. ________________
10. ________________
11. ________________
12. ________________
13. ________________
14. ________________
Proofs
1. GIVEN: B is the midpoint of [pic].
B is the midpoint of [pic].
PROVE: (ABD ( (EBC
2. GIVEN: [pic]; [pic] ,
PROVE: (ABC ( (DCB
3. GIVEN: O is the midpoint of [pic]; [pic]
PROVE: [pic]
4. GIVEN: [pic]; [pic][pic]
PROVE: [pic]
5. GIVEN: [pic],
[pic]
PROVE: [pic]
[pic]
[pic]
5.
6.
Answers
1. _________________
2. _________________
3. ________________
4. ________________
5. ________________
6. ________________
7. ________________
8. ________________
9. ________________
10. ________________
11. ________________
12. ________________
In [pic] and [pic].
19. Name a median of [pic].
20. Name an altitude of [pic].
21. Name an angle bisector of [pic].
22. If [pic]is a median, [pic] and [pic]find [pic]
Answers
13. _________________
14. _________________
15. ________________
16. ________________
17. ________________
18. ________________
19. ________________
20. ________________
21. ________________
22. ________________
1. _________________
2. ________________
3. ________________
4. ________________
5. ________________
6. ________________
7. ________________
8. ________________
9. ________________
10. ________________
11. ________________
12. ________________
13. ________________
14. ________________
15.
21. A tree casts a shadow of 48 feet. Nancy, who id 5 feet tall, casts a shadow of 9 feet. About how tall is the tree?
22. On a map of the Unites Sates [pic] inches represents 810 miles. If it is approximately [pic] inches from Miami to Dallas on the map, what is the actual distance in miles?
15. ________________
16. ________________
17. ________________
18. ________________
19. ________________
20. ________________
21. ________________
22. _________________
-----------------------
B
A
C
D
F
E
Q
[pic]
R
T
[pic]
S
EG
FG
GF
GI
HI.
EF
HI
JG
EF
[pic]
[pic]
A
B
C
D
[pic]
[pic]
G
B
A
3
2
F
4
1
H
C
7
5
D
6
E
[pic]
[pic]
2
1
5
4
3
8
7
6
12
11
10
16
15
9
[pic]
14
13
A
B
[pic]
[pic]
[pic][pic]
[pic]
[pic]
[pic]
E
D
6
5
4
3
1
2
C
B
A
13
12
10
11
7
9
8
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
6
8
2
[pic]
5
4
3
1
7
[pic]
[pic]
[pic]
Y
[pic]
W
D
[pic]
X
E
F
AB
M
N
O
P
Q
Z
V
Y
U
W
X
A
R
Q
P
C
B
................
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