Geometry – Final Exam Review
Unit 3
Name: _____________________
Date: _________ Period: ______
In problems 1- 3, use the cube to name each of the following.
1. all lines that are parallel to BC
2. a pair of parallel planes
3. two lines that a skew to AE
Use the diagram on the right for questions 4-5
4. Identify all pairs of each type of angles in the diagram.
a. corresponding angles
b. alternate interior angles
c. same-side interior angles
d. alternate exterior angles
5. True or False. Explain.
a. 𝑚∠3 ≅ 𝑚∠7
c. 𝑚∠4 + 𝑚∠6 = 180
b. 𝑚∠2 ≅ 𝑚∠3
d. 𝑚∠5 + 𝑚∠6 = 180
Use the diagram on the right for questions 6-7
6. Identify all pairs of each type of angles in the diagram.
a. corresponding angles
b. alternate interior angles
c. same-side interior angles
d. alternate exterior angles
7. True or False. Explain.
a. 𝑚∠3 ≅ 𝑚∠8
c. 𝑚∠2 ≅ 𝑚∠5
b. 𝑚∠5 = 130°
d. 𝑚∠6 = 50°
In problems 8-9, find m1 and m2 and state the theorems or postulates that justify your answers.
8.
9.
In problem 10 find the value of x and the measure of each labeled angle.
10.
11. Find the value of x for which a || b.
Use the diagram on the right for questions 12-14. Fill in the blank.
12. ∠5 𝑎𝑛𝑑 ∠7 are a pair of__________________ angles. If lines d and e
are parallel then ∠5 𝑎𝑛𝑑 ∠7 are ___________________.
13. ∠8 𝑎𝑛𝑑 ∠7 are a pair of__________________ angles. If lines b and c
are parallel then ∠8 𝑎𝑛𝑑 ∠7 are ___________________.
14. If lines d and e are parallel then 𝑚∠3 + 𝑚∠4 =__________________.
Fill in the missing part of the theorems/postulates for questions 15-18.
15. If two parallel lines are cut by a transversal then alternate exterior angles are ________________.
16. Vertical angles are __________________.
17. If ____________________________________ then corresponding angles are congruent.
18. If two lines and a transversal form same side interior angles that are supplementary then
__________________________________________.
19. In a plane, 𝑐 ⊥ 𝑏, 𝑏 ⊥ 𝑑 𝑎𝑛𝑑 𝑑 ⊥ 𝑎. Draw a picture to represent this situation. What is the
relationship between lines c and d?
For problems 20-21, find m1.
20.
21.
For problems 22-23, find the value of each variable.
22.
23.
For problems 24-28, use the given information to write and equation of each line.
24. slope -4, y-intercept 6
25. slope 7, passes through (1, -2)
26. passes through (4, 2) and (6, -3)
27. Write the equation of the line parallel to y =
1
x + 3 through (6, 3).
2
28. Write the equation of the line perpendicular to y = x + 2 through (3, 2).
29. What is the slope of a line parallel to -8x + y = 2?
a)
b)
c)
d)
8
8
-1
-1
8
1
8
30. Given m2 = 50, which postulate or theorem proves m4 = 50?
a)
b)
c)
d)
Alternate Interior Angles Theorem
Corresponding Angles Postulate
Parallel Postulate
Same-Side Interior Angles Theorem
31. Given: m || n
Prove: m1 + m7 = 180