Geometry
Name ______________________
Period ___________
Date ___________
Chapter 3 Summary and Review
Section 3.1: Identify Pairs of Lines and Angles:
1. Parallel Lines
 How do we label a pair of parallel lines?
 Name a pair of parallel lines from the diagram.
2. Intersection Lines
 Name a pair of intersecting lines from the diagram.
3. Perpendicular Lines
 Two lines are perpendicular if _____________________________________
 How do we label a pair of perpendicular lines?
 Name a pair of perpendicular lines from the diagram.
4. Skew Lines
 Two lines are skew if _______________________________________________
 Name a pair of skew lines from the diagram.
5. Parallel Plane
 Parallel planes are two planes that _____________________________________
 Name 2 parallel planes from the diagram.
6. Transversal
 Transversal is line that ___________________________
 Name the transversal in the diagram:
Based on the figure to the right, name the following:
7. A pair of parallel lines
8. A pair of skew lines
9. A pair of perpendicular lines
10. Two parallel planes
11. Two perpendicular planes
12. Corresponding Angles
 Name a pair of corresponding angles from the diagram below: _____ _____
13. Alternate Interior Angles
 Name 2 alternate interior angles on the diagram below:
_____ _____
14. Alternate Exterior Angles
 Name 2 alternate exterior angles on the diagram below:
_____ _____
15. Consecutive Interior Angles
 Name 2 consecutive interior angles on the diagram below:
_____ _____
16. Classify each pair of angles (use the letter). Some letters may be used more than once.
a) ∠5 and ∠8 ____
A. Corresponding
b) ∠3 and ∠7 ____
B. Alternate Interior
c) ∠2 and ∠5 ____
C. Alternate Exterior
d) ∠4 and ∠6 ____
D. Consecutive Interior
e) ∠3 and ∠8 ____
E. Linear Pair
f) ∠3 and ∠5 ____
F. Vertical Angles.
g) ∠1 and ∠3 ____
Section 3.2: Use Parallel Lines and Transversals
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
Write the converse:
If two lines are cut by a transversal and corresponding angles are congruent, then the two lines are parallel.
Alternate Interior Angles Theorem
If _______________________ are cut by a ______________, then the ___________________________ are
_________________.
Write the converse:
Alternate Exterior Angles Theorem
If _______________________ are cut by a ______________, then the ___________________________ are
_________________.
Write the converse:
Consecutive Interior Angles Theorem
If _______________________ are cut by a ______________, then the ___________________________ are
_________________.
Write the converse:
17.
Find the measure of the missing angles.
m 1  _______
m  2  _______
m  3  _______
m  4  _______
Is there enough information to prove that line p || line q? If so, state the theorem or postulate you would use.
18.
20.
19.
Find the measure of the missing angles. Lines p and q are not parallel.
m∠1 ________
m ∠2 ________
m∠3 ________
m ∠4 ________
m ∠5 ________
p
60 1
4 5
q
2
3
100
Use the diagram and the given information to determine if m || n , n || p , p || m or none.
21.  1   12
22.  3   6
23.  9   5
24.  12   9
m
n
25. m  4 + m  6 = 180o
p
Find the value of x that makes lines m and n parallel.
1 2
3 4
5 6
7 8
9 10
11 12
26.
27.
Section 3.4: Find and Use Slopes of Lines
28. Explain the slope of a non-vertical line.
29. List the four types of slopes of lines in the Coordinate Plane:
30. Slopes of Parallel Lines are ____________________________
31. What is the symbol used that means parallel? _______________
32. Find the slope of the line containing the given points:
 1,  4
and 1, 3
m = _____________
3,  2
and
 1,  4
m = _________________
Find the slope for lines k1 and k2 then determine if they are parallel.
33. Slopes of Perpendicular Lines are _________________________
What is the symbol used that means perpendicular? ___________
Find the slope of line h then draw a perpendicular line to line h
Through point P.
Section 3.5: Write and Graph Equations of Lines
 3, 5
and  6, 5
m = _____________
34. What is the slope-intercept form of the linear equation? ________________________
35. What is the standard form of the linear equation? _____________________________
36. What is the point-slope form of the linear equation? ___________________________
37. Decide if the following pairs of lines are parallel, perpendicular or neither.
1
y x2
3
1
y  x 1
3
_______________
y  2x
y  2x  7
y  3
x3
________________
________________
Write an equation of the line that passes through the given point P and has the given slope m. Leave your equation in
any form.
38. P ( 3, 2); m =
1
39.
3
P (3, 1); m = -4
Write an equation for a line with the given information:
40. Parallel to y 
3
x  5 passing through the point  2, 1
4
41. Perpendicular to line l passing through  0 , 4
l
Graph the following lines. Show at least two points.
42. 3 x  2 y  6
43. y  1 
2
 x  2
3
Section 3.6: Prove Theorems About Perpendicular Lines
44. y  2
Sketch the following situations:
45. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
46. If two lines are perpendicular, then they intersect to form four right angles.
47. If two sides of adjacent acute angles are perpendicular, then the angles are complementary.
48. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
49. In a plane, if two lines are perpendicular to the same line, then they are parallel.
50. Lines a and b are perpendicular. Find the value of x.
x = _____________
a
60o
(2X)0
b