Name: ________________________________________________ Class: ______________ Date: ____________________
Geometry Chapter 3 Exam
Multiple Choice (3 points each)
Identify the letter of the choice that best completes the statement or answers the question.
Refer to the figure below for #1-4.
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive
interior angles.
____ 1. ∠4and ∠6
a. alternate interior
b. alternate exterior
c. corresponding
d. consecutive interior
____ 2. ∠2 and ∠11
a. alternate interior
b. alternate exterior
c. corresponding
d. consecutive interior
____ 3. ∠3and ∠7
a. alternate interior
b. alternate exterior
c. corresponding
d. consecutive interior
____ 4. ∠8and ∠9
a. alternate interior
b. alternate exterior
c. corresponding
d. consecutive interior
Name: ________________________________________________ Class: ______________ Date: ____________________
Refer to the figure below for #5-7.
____ 5. Which of the following segments is NOT skew to 𝐷𝐶 ?
a. 𝐸𝐻
b. 𝐵𝐹
c. 𝐴𝐸
d. 𝐸𝐹
____ 6. Which of the following segments does NOT intersect 𝐴𝐸 ?
a. 𝐺𝐻
b. 𝐴𝐵
c. 𝐸𝐹
d. 𝐸𝐻
____ 7. Which of the following planes is parallel to plane BCG?
a. EFG
b. ADH
c. ABC
d. CDH
Name: ________________________________________________ Class: ______________ Date: ____________________
Refer to the figure below for #8 and #9.
In the figure, 𝑎 ∥ 𝑏, 𝑚∠4 = 120, and 𝑚∠9 = 75.
____ 8. Find the measure of ∠16.
a. 120
b. 75
c. 105
d. 60
____ 9. Find the measure of ∠1.
a. 120
b. 75
c. 105
d. 60
Refer to the figure below for #10 and #11.
In the figure, 𝑡 ∥ 𝑢, 𝑚∠2 = 55, 𝑎𝑛𝑑 𝑚∠16 = 100.
____ 10. Find the measure of ∠8.
a. 100
b. 80
c. 125
d. 55
Name: ________________________________________________ Class: ______________ Date: ____________________
____ 11. Find the measure of ∠9.
a. 100
b. 80
c. 125
d. 55
Refer to the figure below for #12.
____ 12. In the figure, 𝑎 ∥ 𝑏. Find 𝑚∠1.Hint: Draw an auxiliary line. (Show all work).
a. 155
b. 65
c. 40
d. 90
Refer to the figure below for #13.
____ 13. In the figure, 𝑐 ∥ 𝑑. Find 𝑚∠1.Hint: Draw an auxiliary line. (Show all work).
a. 55
b. 25
c. 155
d. 305
Name: ________________________________________________ Class: ______________ Date: ____________________
Determine the slope of the line that contains the given points. Show all work.
____ 14. 𝑀 2, 5 , 𝑁 5, −4
a. -3
1
b. − 3
c. 7
1
d. 7
____ 15. 𝑀 −4, 1 , 𝑁 3, −1
2
a. − 7
7
b. −
2
c. 0
d. undefined
Determine whether 𝑅𝑆 𝑎𝑛𝑑 𝑇𝑈 are parallel, perpendicular, or neither. Use the slope formula and
show all work.
____ 16. 𝑅
a.
b.
c.
3, 5 , 𝑆 5, 6 , 𝑇 −2, 0 , 𝑈 4, 3
parallel
perpendicular
neither
____ 17. 𝑅
a.
b.
c.
−2, 5 , 𝑆(−4, 1), 𝑇 3, 3 , 𝑈 1, 5
parallel
perpendicular
neither
____ 18. 𝑅
a.
b.
c.
−1, 4 , 𝑆(−3, 7), 𝑇 5, −1 , 𝑈 8, 1
parallel
perpendicular
neither
Write an equation in slope-intercept form of the line that satisfies the given conditions. Show work
for #20.
1
____ 19. 𝑚 = 3, 𝑏 = − 4
1
a. 𝑦 = − 4 𝑥 + 3
1
b. 𝑦 = 4 − 3
1
c. 𝑦 = 3𝑥 + 4
1
d. 𝑦 = 3𝑥 − 4
Name: ________________________________________________ Class: ______________ Date: ____________________
____ 20. 𝑚 = 3, contains (−2, 4)
a. 𝑦 = 3𝑥 − 2
b. 𝑦 = 3𝑥 + 10
c. 𝑦 = 3𝑥 + 4
d. 𝑦 = −2𝑥 + 4
Write an equation in point-slope form of the line that satisfies the given conditions.
____ 21. 𝑚 = −4, contains (0, 3)
a. 𝑦 = −4(𝑥 − 3)
b. 𝑦 − 3 = −4𝑥
c. 𝑦 + 4 = 3𝑥
d. 𝑦 − 4 = 3𝑥
2
____ 22. 𝑚 = 3 , contains (5, −7)
2
a. 𝑦 + 7 = 3 (𝑥 − 5)
2
b. 𝑦 − 5 = 3 (𝑥 + 7)
2
c. 𝑦 − 7 = 3 (𝑥 + 5)
2
d. 𝑦 + 5 = 3 (𝑥 − 7)
____ 23. Write an equation in slope-intercept form of the line that contains (7, −2) and is parallel
to 2𝑥 − 5𝑦 = 8.
5
2
a. 𝑦 = − 𝑥 −
2
2
7
b. 𝑦 = 5 𝑥 − 2
5
c. 𝑦 = − 2 𝑥 − 2
2
d. 𝑦 = 5 𝑥 −
24
5
Name: ________________________________________________ Class: ______________ Date: ____________________
Refer to the figure below for #24 and #25.
Given the following information, determine which lines, if any, are parallel. State the postulate or
theorem that justifies your answer.
____ 24. ∠2 ≅ ∠10
a. 𝑎 ∥ 𝑏; congruent corresponding angles
b. 𝑎 ∥ 𝑏; congruent alternate interior angles
c. 𝑐 ∥ 𝑑; congruent corresponding angles
d. 𝑐 ∥ 𝑑; congruent alternate interior angles
____ 25. 𝑚∠2 + 𝑚∠3 = 180
a. 𝑎 ∥ 𝑏; consecutive interior angles are supplementary
b. 𝑎 ∥ 𝑏; corresponding angles are supplementary
c. 𝑐 ∥ 𝑑; consecutive interior angles are supplementary
d. 𝑐 ∥ 𝑑; corresponding angles are supplementary
Find the distance between the pair of parallel lines. Show all work.
____ 26. 𝑦 = 2𝑥 + 2
𝑦 = 2𝑥 − 3
a. 10
a. 5
b. 10
c. 5
____ 27.
𝑦 = 3𝑥 + 12
a. 10
b. 3 10
c.
5
d. 3 5
𝑦 = 3𝑥 − 18
Name: ________________________________________________ Class: ______________ Date: ____________________
Short Answer (3 points each)
28. In the figure, 𝑚 ∥ 𝑛. Find x and y.
29. Find x and 𝑚∠𝐺𝐻𝐼 so that 𝑚 ∥ 𝑛.