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

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3. 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. Definition of Alternate Interior Angles 1 2 3 4 5 6 7 8

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

5. 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. Alternate Exterior Angles 1 2 3 4 5 6 7 8

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

7. 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. Same-side or Consecutive Interior Angles 1 2 3 4 5 6 7 8

8. 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? Corresponding Angles 1 2 3 4 5 6 7 8

9. 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. Corresponding Angles 1 2 3 4 5 6 7 8

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

11. If two lines are parallel, prove alternate interior angles are congruent. Given: m  n Prove:  4   5 Prove alternate interior angles are congruent. 12 3 4 5 6 7 8 n m m  n Given

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

13. If m  n and a  b, find all the angles congruent to  6. Congruent Angles Activity 1 2 3 4 5 6 7 8 910 11 12 13 14 1516 m n ab

14. If m  n and a  b, find all the angles congruent to  6.  2,  3,  7,  10,  11,  14,  15 Congruent Angles Activity 1 2 3 4 5 6 7 8 910 11 12 13 14 1516 m n ab

15. Given m  n, find the value of x. 104  (5x+4)  68  m n

16. 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 Create Your Own

17. 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. Create Your Own

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