Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Right Triangles and Trig

9-12

45 Minutes

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

TI-Nspire™
TI-Nspire™ CAS

3.9

## Special Right Triangles

#### Activity Overview

Examine two types of special right triangles and determine the predictable relationships between the lengths of their legs and hypotenuse.

#### Objectives

• Students will identify the relationship between the lengths of the shorter and longer legs in a 30°-60°-90° right triangle.
• Students will determine the relationship between the shorter leg and the hypotenuse in a 30°-60°-90° right triangle.
• Students will identify the relationship between the lengths of the legs in a 45°-45°-90° right triangle.
• Students will determine the relationship between the legs and the hypotenuse in a 45°-45°-90° right triangle.

#### Vocabulary

• hypotenuse
• altitude
• right triangle

#### About the Lesson

This lesson involves manipulating a special right triangle that is half of an equilateral triangle (the 30°-60°-90° triangle) and a special right triangle that is half of a square (the 45°-45°-90° triangle). As a result, students will: Determine the relationships among the lengths of the sides of a 30°-60°-90° triangle and a 45°-45°-90° triangle.