1. Recall Vertical Angles are Congruent
Daily Warm Up
Recall Vertical Angles are Congruent
Find the measure of the given angles.
Classify the angle pair as corresponding, alternate interior, alternate exterior, consecutive interior, or no relationship
2x + 13 z y
x + 24 z s

2. Parallel Lines & Transversals Notes 3.2
Goals:
Use properties of parallel lines
Prove theorems about parallel lines
Solve real-life problems

3. Recall Core Concept Transversal
A line that intersects two or more coplanar lines at different points
Line t is a transversal intersecting line m & line n. t m n

4. Recall Core Concept Corresponding Angles
Two angles that have corresponding positions. t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
On the same side of the transversal and both on the same side of each angles respective side
<4 & <8 are corresponding angles
<1 & <5; <2 & <6; <3 & <7

5. Recall Core Concept Alternate Exterior Angles
Two angles that lie outside the two lines & on opposite sides of the transversal t. t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
Both angle pairs alternate the side of the transversal they lie on & they both lie on the outside of
line m & line n
<8 & <2 are alternate interior angles or <1 & <7

6. Alternate Interior Angles
Recall Core Concept
Alternate Interior Angles
Two angles that lie between the two lines & on opposite sides of the transversal t t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
<4 ≅ <6
<3 ≅ <5

7. Recall Core Concept Consecutive Interior Angles “same side interior”
Two angles that lie between the two lines and on the same side of the transversal t. t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
Both angle pairs are both on the same side of the transversal & in between line m & line n
<4 & <5 are same side interior angles
<3 & <6 are consecutive interior angles

8. Corresponding Angles Theorem
Core Concept
Corresponding Angles Theorem
Theorem 3.1I
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
<4 ≅ <8
<1 ≅ <5
<2 ≅ <6
<3 ≅ <7

9. Alternate Exterior Angles Theorem
Core Concept
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
<8 ≅ <2
<1 ≅ <7

10. Alternate Interior Angles Theorem
Core Concept
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
<4 ≅ <6
<3 ≅ <5

11. Consecutive Interior Angles Theorem “same side interior”
Core Concept
Consecutive Interior Angles Theorem “same side interior”
If two parallel lines are cut by a transversal, then the pairs of Consecutive Interior angles are Supplementary. t m 2 1 3 4
Use popsicle sticks to have different students give an angle pair n 6 5 8 7
<4 ≅ <5
<3 ≅ <6

12. Using the Corresponding Angles Theorem
Example 1.
Using the Corresponding Angles Theorem
The measures of three of the numbered angles are 120°. Identify the angles. Explain your Reasoning.
Have students work together in groups of two for 3 minutes on naming these angles.

13. Using Properties of Parallel Lines
Example 2.
Using Properties of Parallel Lines
Find the value of x.
Have students work together in groups of two for 3 minutes on naming these angles.

14. Using Properties of Parallel Lines
Example 3.
Using Properties of Parallel Lines
Find the value of x.
Have students work together in groups of two for 3 minutes on naming these angles.

15. Solving a Real-Life Problem
Example 4.
Solving a Real-Life Problem
When sunlight enters a drop of rain, different colors of light leave the drop at different angles. This process is what makes a rainbow. For violet light, m<2 = 40°. What is m<1? How do you know?
Have students work together in groups of two for 3 minutes on naming these angles.

16. Practice Extra Practice – In Class Worksheet
Hw # 16 part 2– Big Ideas TB
Pg. 135 #1-12, 17, 18, 23, 25-28
Quick review student’s don’t need to write down again.