Report

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). 2 1 3 4 5 6 7 8 Angles 4 and 5 are also alternate interior angles. Alternate Exterior Angles Based on what you know about alternate interior angles, which angles would be alternate exterior angles? 2 1 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? 2 1 3 4 5 6 7 8 Angles 1 and 8 are alternate exterior angles. Angles 2 and 7 are alternate exterior angles. 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? 2 1 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? 2 1 3 4 5 6 7 8 Angles 3 and 5 are same-side interior angles. Angles 4 and 6 are same-side interior angles. 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? 2 1 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? 2 1 3 4 5 6 7 8 Angles 3 and 7, angles 2 and 6, and angles 4 and 8 are also pairs of corresponding angles. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent. 2 1 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 m n Given m n 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 Answers may vary. m n Given 1 5 Corresponding angles are congruent. 1 4 Vertical angles are congruent. 4 5 Substitution m n 1 2 3 4 5 6 7 8 Congruent Angles Activity If m n and a b, find all the angles congruent to 6. a b 1 2 3 4 9 10 11 12 5 6 7 8 13 14 15 16 m n Congruent Angles Activity If m n and a b, find all the angles congruent to 6. 2, 3, 7, 10, 11, 14, 15 a b 1 2 3 4 9 10 11 12 5 6 7 8 13 14 15 16 m n Given m n, find the value of x. m 68 n 104 (5x+4) 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 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. For information about Insight 360™, visit http://www.einstruction.com. For additional content samples, click here.