Semester 1 Midterm A

Name:______Date:______

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. What is the name of the ray that is opposite ?

A. B. C. D.

____ 2. What is the intersection of plane STXW and plane SVUT?

A. B. C. D.

____ 3. If find the values of x, EF, and FG. The drawing is not to scale. E F G

A. x = 10, EF = 8, FG = 15 C. x = 10, EF = 32, FG = 45 B. x = 3, EF = –6, FG = –6 D. x = 3, EF = 8, FG = 15

____ 4. What segment is congruent to ? A B C D E

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

A. B. C. D. none

____ 5. If T is the midpoint of what are ST, TU, and SU?

9 x 5x + 28

A. ST = 7, TU = 63, and SU = 126 C. ST = 18, TU = 18, and SU = 36 B. ST = 80, TU = 80, and SU = 160 D. ST = 63, TU = 63, and SU = 126

____ 6. Name an angle adjacent to

A. B. C. D.

____ 7. and are a linear pair. , and . Find the measure of each angle. A. C.

____ 8. Find the coordinates of the midpoint of the segment whose endpoints are H(6, 4) and K(2, 8). A. (4, 4) B. (2, 2) C. (8, 12) D. (4, 6)

____ 9. M is the midpoint of for the points C(3, 7) and F(5, 5). Find MF. A. 2 B. 2 2 C. 2 D. 4

____ 10. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. A. 11 B. 7.8 C. 61 D. 14.9 ____ 11. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8. A. 24 B. 40 C. 12 D. 26

____ 12. What is the value of x? Identify the missing justifications.

, , and .

Q S Drawing not to scale

a. ______x – 5 + x – 7 = 100 b. Substitution Property 2x – 12 = 100 c. Simplify 2x = 112 d. ______x = 56 e. Division Property of Equality

A. Angle Addition Postulate; Subtraction Property of Equality B. Angle Addition Postulate; Addition Property of Equality C. Protractor Postulate; Addition Property of Equality D. Protractor Postulate; Subtraction Property of Equality

____ 13. bisects = 7x. = . Find A. 108 B. 72 C. 180 D. 252 ____ 14. Name the Property of Equality that justifies this statement:

If l = m, then . A. Multiplication Property C. Subtraction Property B. Symmetric Property D. Transitive Property

____ 15. Complete the two-column proof.

Given:

Prove:

A. a. Given C. a. Given b. Substitution Property b. Symmetric Property of Equality c. Addition Property of Equality c. Addition Property of Equality d. Division Property of Equality d. Division Property of Equality e. Symmetric Property of Equality e. Reflexive Property of Equality B. a. Given D. a. Given b. Substitution Property b. Substitution Property c. Addition Property of Equality c. Addition Property of Equality d. Addition Property of Equality d. Division Property of Equality e. Symmetric Property of Equality e. Reflexive Property of Equality ____ 16. Which angles are corresponding angles?

A. C. B. D. none of these

____ 17. Line r is parallel to line t. Find m 6. The diagram is not to scale.

r 7 138° 1 3

t 4 2 5 6

A. 32 B. 138 C. 142 D. 42

____ 18. Which is a correct two-column proof?

Given:

Prove: and are supplementary.

a b r c d

e f s g h

D. none of these

____ 19. Find The diagram is not to scale.

Q R 77°

A. 66 B. 56 C. 124 D. 103 ____ 20. Find The diagram is not to scale.

P >> g

106° >> h

A. 106 B. 74 C. 64 D. 84

____ 21. The expressions in the figure below represent the measures of two angles. Find the value of x. . The diagram is not to scale.

2 x + 36 g

A. 15 B. 17 C. –16 D. 16 ____ 22. Find the values of x and y. The diagram is not to scale.

51° (x – 5)° (y – 6)° 72°

A. x = 51, y = 63 C. x = 63, y = 77 B. x = 77, y = 63 D. x = 77, y = 65 ____ 23. What is the slope of the line shown? y 10 8 6 4 (–2, 2) 2

–10 –8 –6 –4 –2 2 4 6 8 10 x –2 –4 –6 –8 (4, –9) –10

A. 6 C. 11  11 6

B. 6 D. 11  11 6 ____ 24. What is the graph of ? A. y C. y 8 8 6 6 4 4 2 2

–8 –6 –4 –2 2 4 6 8 x –8 –6 –4 –2 2 4 6 8 x –2 –2 –4 –4 –6 –6 –8 –8

B. y D. y 8 8 6 6 4 4 2 2

–8 –6 –4 –2 2 4 6 8 x –8 –6 –4 –2 2 4 6 8 x –2 –2 –4 –4 –6 –6 –8 –8

____ 25. Write an equation in slope-intercept form of the line through point P(6, –1) with slope 4. A. y = 4x – 1 C. y + 1 = 4(x – 6) B. y = 4x – 25 D. y + 6 = 4(x – 1) ____ 26. Write an equation in point-slope form of the line through point J(4, –4) with slope 4. A. C.

____ 27. What is an equation for the line that passes through points (4, –4) and (8, 4)? A. (y – 4) = 2(x + 4) C. (y – 4) = –2(x + 4) B. (y + 4) = 2(x – 4) D. (y + 4) = –2(x – 4) ____ 28. What is an equation in slope-intercept form for the line given? y 8

(5, 1) –8 8 x (–4, –2)

____ 29. Which two lines are parallel? I.

A. II and III C. I and III B. I and II D. No two of the lines are parallel. ____ 30. Are the lines y = –x – 2 and 4x + 4y = 16 perpendicular? Explain. A. Yes; their slopes have product –1. B. No; their slopes are not opposite reciprocals. C. Yes; their slopes are equal. D. No; their slopes are not equal Short Answer

1. What is the value of x? Identify the missing justifications.

2. What is the value of x? Justify each step. 3. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.

Given:

Prove:

4. State the missing reasons in this proof. Given:

Prove: q

1 2 p 3 4

5 6 r 7 8

1. Write a two-column proof.

Given: are supplementary.

Prove: 1 2 3 4 l

5 6 7 8 m

Semester 1 Midterm Answer Section

MULTIPLE CHOICE

1. C 2. B 3. A 4. B 5. D 6. B 7. B 8. D 9. C 10. B 11. C 12. B 13. D 14. B 15. A 16. C 17. D 18. A 19. B 20. B 21. D 22. B 23. C 24. C 25. B 26. B 27. B 28. A 29. A 30. B

SHORT ANSWER

1. a. Angle Addition Postulate b. Substitution Property c. Distributive Property d. Simplify e. Addition Property of Equality f. Division Property of Equality 2. a. Segment Addition Postulate b. Substitution c. Simplify d. Subtraction Property of Equality e. Division Property of Equality 3. a. Corresponding angles b. Vertical angles c. Transitive Property 4. a. Vertical angles. b. Transitive Property. c. Alternate Interior Angles Converse.

1. [4]

[3] correct idea, some details inaccurate [2] correct idea, some statements missing [1] correct idea, several steps omitted