1. Alternate Interior Angles High School Geometry
Aligned to Common Core State Standards

2. Teacher Notes
Insight 360™ is eInstruction’s classroom instruction system that allows you to interact with your students as they learn, quickly gaining insight into student understanding during class so you can adjust instruction in real-time during a single class session.
Use this content, designed specifically for use with Insight 360™, to interact with your class. This content includes brief instructional material and two types of activities:
Constructed Response Activity for students to complete as an individual or a group assignment. Send each Constructed Response Activity to the Insight 360 iPad Student App.
Assessment Item with CueTag™ for students to respond to via student response devices. Receive instant real-time feedback and longitudinal reports.

3. Definition of Alternate Interior Angles
Two angles that lie between two lines and on the opposite sides of a third line are called alternate interior angles.
In the drawing below, 3 and 6 would be alternate interior angles since they are inside the blue parallel lines and on opposite (alternate) sides of the transversal (red line).
Angles 4 and 5 are also alternate interior angles. 1 2 3 4 5 6 7 8

4. Alternate Exterior Angles
Based on what you know about alternate interior angles, which angles would be alternate exterior angles? 1 2 3 4 5 6 7 8

5. Alternate Exterior Angles
Based on what you know about alternate interior angles, which angles would be alternate exterior angles?
Angles 1 and 8 are alternate exterior angles.
Angles 2 and 7 are alternate exterior angles. 1 2 3 4 5 6 7 8

6. Same-side or Consecutive Interior Angles
Based on what you know about alternate interior angles, which angles would be same-side or consecutive interior angles? 1 2 3 4 5 6 7 8

7. Same-side or Consecutive Interior Angles
Based on what you know about alternate interior angles, which angles would be same-side or consecutive interior angles?
Angles 3 and 5 are same-side interior angles.
Angles 4 and 6 are same-side interior angles. 1 2 3 4 5 6 7 8

8. Corresponding Angles
Corresponding angles lie on corresponding sides of the two lines and on the same side of the third line. Angles 1 and 5 are corresponding angles. What other pairs of angles are corresponding angles? 1 2 3 4 5 6 7 8

9. Corresponding Angles
Corresponding angles lie on corresponding sides of the two lines and on the same side of the third line. Angles 1 and 5 are corresponding angles. What other pairs of angles are corresponding angles?
Angles 3 and 7, angles 2 and 6, and angles 4 and 8 are also pairs of corresponding angles. 1 2 3 4 5 6 7 8

10. Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then corresponding angles are congruent. 1 2 3 4 5 6 7 8

11. Prove alternate interior angles are congruent.
If two lines are parallel, prove alternate interior angles are congruent.
Given: m  n
Prove: 4  5 1 2 3 4 5 6 7 8 n m
m  n
Given
Assumes you have proven that corresponding angles are congruent.

12. Prove alternate interior angles are congruent.
If two lines are parallel, prove alternate interior angles are congruent.
Given: m  n
Prove: 4  5
Answers may vary. 1 2 3 4 5 6 7 8 m n
m  n
Given
1  5
Corresponding angles are congruent.
1  4
Vertical angles are congruent.
4  5
Substitution

13. Congruent Angles Activity
If m  n and a  b, find all the angles congruent to 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 m n a b
Assumes you have proven that corresponding angles are congruent.

14. Congruent Angles Activity
If m  n and a  b, find all the angles congruent to 6.
2, 3, 7, 10, 11, 14, 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 m n a b
Assumes you have proven that corresponding angles are congruent.

15. Given m  n, find the value of x.
104
(5x+4)
68 m n
Assumes students know that base angles of an isosceles triangle are congruent. Therefore the angle adjacent to the x degree angle is also 68. The vertex angle for that triangle would then be 44. The 44 and the angle of x are alternate interior angles and therefore congruent.

16. Create Your Own
Create your own problem to find a missing angle measure using parallel lines and alternate interior angles. Your problem must include the following:
a diagram
given information
3 or more steps to solve
Note to teacher: Solve each student’s problem as a class.

17. Create Your Own
Create your own problem to find a missing angle measure using parallel lines and alternate interior angles. Your problem must include the following:
a diagram
given information
3 or more steps to solve
Answers will vary.
Note to teacher: Solve each student’s problem as a class.

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