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

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.

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

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

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

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

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

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

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

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

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.

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

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.

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.

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.

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.

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.

For information about Insight 360™, visit http://www.einstruction.com. For additional content samples, click here.