1. Parallel Lines and Transversals
Chapter 3 Section 3.3
Parallel Lines and Transversals

2. Warm-Up What can you conclude about the angles?
Which is not true if m<2=90?
The lines are perpendicular.
<1 is a right angle.
The unlabeled angles are congruent.
<1 and <2 are complementary . 1 2

3. When two parallel lines are cut by a transversal, then …
Corresponding angles are 
Corresponding Angle Postulate
Alternate Interior angles are 
Alternate Interior Angle Theorem.
Alternate Exterior angles are 
Alternate Exterior Angle Theorem
Consecutive Interior angles are Supplementary
Consecutive Interior Angle Theorem

4. Perpendicular Transversal Thm.
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

5. Find the measure of 1 and 2 Explain your reasoning
Corresponding angle Postulate
m 2 = 118
Alternate Exterior angle theorem
m 1 = 72
Alternate Interior angle theorem
m 2 = 180 – 72 = 108
Consecutive Interior angle theorem

6. Find the measure of 1 and 2 Explain your reasoning
Vertical Angle Theorem
m 2 = 127
Corresponding angle Postulate

7. Find the value of x and y and state the reason
Vertical Angle Thm
y = 81
Corresponding Angle Postulate
x = 180 – 98 = 82
Form a linear pair and are supplementary
y = 82
Alternate Exterior angle theorem

8. Find the value of x and y and state the reason
Perpendicular Transversal Thm
y = 90
If two lines are perpendicular then they form 4 right angles

9. Find the value of x and state the reason
Alt. Int. Angle Thm.
5x – 15 = 80
5x = 95
x = 19
Corresponding Angle Postulate
3(x + 9) = 129
3x + 27 = 129
3x = 102
x = 34

10. Find the value of x and state the reason
Cons. Int. Angle Thm.
4x – = 180
4x + 66 = 180
4x = 114
x =

11. Complete the flow proof of the Proof of the Alt. Ext. Angle Thm.
a: Given
b: Corresponding Angle Postulate
c: Vertical Angle Thm
d: Transitive