# Activities

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• • ##### Subject Area

• Math: Geometry: Similarity and Proportion

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ Apps for iPad®
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

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Angles and Similarity

#### Activity Overview

Experiment with the measures of the angles of similar triangles to determine conditions necessary for two triangles to be similar.

#### Objectives

• Students will be able to prove that when two pairs of corresponding angles of two triangles are congruent, the third pair of angles will be congruent.
• Students will recognize and apply the Angle-Angle Similarity Theorem.

#### Vocabulary

• proportional
• similarity
• congruence
• corresponding parts

#### About the Lesson

This lesson involves investigating the relationship among angles in similar triangles. As a result students will:

• Change the angle measures of one triangle to match the angle measures in another triangle.
• Prove that when two pairs of corresponding angles of two triangles are congruent, the third pair of angles will be congruent.
• See the equal ratios of the sides when two angle measures match showing that the congruence of two pairs of corresponding angles is sufficient to make two similar triangles.
• Apply the ratio of the sides of similar triangles to find the measure of one side when they know the measure of a given corresponding side.