Geometry
Review Chapter 3
Name _________________________________________
Use the picture at the right for Questions #1 – 8.
True or False.
1.
 1 and  9 are vertical angles. ________
2.
 8 and  15 are alternate interior angles. _________
3.
 2 and  4 are same side interior angles. __________
4.
 2 and  13 are alternate interior angles. _________
5.
 15 and  12 are alternate exterior angles. _______
6.
 9 and  7 are corresponding angles. ________
7.
 1 and  11 are corresponding angles. ________
d
c
a a
b
8. Fill in the blanks. Still use the picture at the right.
Given:  1   10
Therefore, line _________ is parallel to line __________ by ________________________________________ theorem.
Find m  1 and then m  2.
9.
10.
 1 = ________  2 = __________
 1 = ________  2 = __________
11.
12.
 1 = ________  2 = __________
 1 = ________  2 = __________
Find the value of x for which l || m.
13.
14.
x = ___________
x = ___________
Find the value of each variable. Show your work.
15.
a) Find the total
interior angles sum.
16.
a) What is the sum of the
exterior angles of this
polygon?
b) Find x, y, and z.
b) Find x.
Find the value of each variable.
17.
18.
x = ________
y = ________
x = _______
y = ________
19a. Find the sum of the interior angles of a 21-gon.
19b. What is the measure of an exterior angle of a regular 20-gon?
20. Find them measure of an interior angle and an exterior angle of a regular 24-gon.
Interior = ________
Exterior = __________
Tell if the lines are parallel, perpendicular or neither. (Hint – don’t forget to get equations into slope-intercept form.)
21.
y=x+3
x+y=3
22.
y = 3x + 4
y – 1 = 3x
23.
y=x+5
y = -5x - 1
Write the equation of the line in any form.
24. slope = -1; P(2, -5)
25. A(3, 8) and B(1, -6)
26. Write an equation of a line that is parallel to
y = 2x – 1 and goes through point (-4, 3).
27. Write an equation of a line that is perpendicular to
y = 31 x + 2 and goes through point (6, 4).
28. Graph the line.
y=
1
3
29. Find the x and y intercepts. Then graph.
x+2
3x + y = 6
8
8
6
6
4
4
2
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-8 -7 -6 -5 -4 -3 -2 -1
-2
-2
-4
-4
-6
-6
-8
-8
1 2 3 4 5 6 7 8
30. True or False.
Given the points: A(-1, 3); B(4, 8); C(-6, 0); D(2, 8), line AB is parallel to CD. ________________
31. Name the vertical angle for <1.
32. Name the alternate interior angle for <4.
33. Name the corresponding angle for <3.
34. Parallel lines are coplanar or noncoplanar?
35. Skew lines are coplanar or noncoplanar?
36. State the formula for the sum of the interior angles of a polygon.
37. What is the sum of the exterior angles of any polygon?
Use the given information to determine which lines must be parallel. State the theorem or postulate that
justifies your answer. If there are no such lines, write none. Hint: Use the tracing method we did in class.
38.
7 and8
Supplementary
Answer:
Justify:
39. 2  11
Answer:
Justify:
40.
3and7
Supplementary
Answer:
Justify:
41. 12  4 Answer:
Justify:
42 5  11
Answer:
Justify:
43. 1  2
Answer:
Justify:
12
Geometry
1. true
5. False
Answers-Review Chapter 3
2. False
6. False
3. true
7. true
4. True
8. line a, line b, converse of alternate interior angles
9.
 1 = 120.  2 = 120
10.
 1 = 75,  2 = 105
11.
 1 = 65,  2 = 65
12.
 1 = 70,  2 = 110
13. x = 5
14. x = 25
15. a) 540
b) x = 109
16. a) 360
b) x = 85, y = 100, z = 100
17. x = 45, y = 45
18. x = 73, y = 45
19a. 3420
19b. 18
20. int = 165, ext = 15
21. perpendicular
22. Parallel
23. neither
24. y = -x – 3 (or) y + 5 = -1(x – 2)
25. y = 7x – 13 (or) y – 8 = 7(x – 3) (or) y + 6 = 7(x – 1)
26. y = 2x + 11 (or) y – 3 = 2(x + 4)
27. y = 3x - 14 (or) y – 4 = 3(x – 6)
28. we will check in class
29. (0, 6) and (2, 0)
30. true
31.
<3
32. <5
33. <7
34. coplanar
35. Noncoplanar
36. 180(n – 2)
37. 360o
38. a || d converse of same-side interior angles
39. l || m converse of alternate exterior angles
40. l || m converse of same-side interior angles
41. l || m converse of alternate interior angles
42. l || m converse of corresponding angles
43. b || c converse of corresponding angles