# Activities

• • • ##### Subject Area

• Math: Geometry: Triangles

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 8 from the EXPLORATIONS Book:
Shaping Middle Grades Mathematics: Activities for Geoboard and the TI-73

## Right Triangles are Cool Because of Pythag's Rule

#### Activity Overview

In this activity, students use the Geoboard to determine the length of the sides of a right triangles.

#### Before the Activity

• Start the Geoboard App and format it
• See the attached PDF file for detailed instructions for this activity
• Print pages 85 - 91 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

• Draw a right triangle with leg lengths of 1 unit and draw squares on each side of the triangle

• Draw right triangles with the different leg lengths given in the table
• Draw surrounding squares and record areas of the squares
• Find the relationship between the areas of the squares
• Understand the Pythagorean Theorem that states - the sum of the square of the length of the legs is equal to the square of the length of the hypotenuse in a right triangle
• Draw a right angle triangle with sides 3 and 4 and find the length of the hypotenuse
• Note the length is 5 units

• Draw four right triangles with length of legs that are different from those used earlier
• Enter leg lengths, hypotenuse length, leg length squared, and hypotenuse squared in different columns
• Find the relationship between the leg length squared and the hypotenuse squared
• Observe that the sum of the leg length squared is equal to the hypotenuse squared and the Pythagorean Theorem is valid in right triangle is A2 + B2 = C2
• Given the length of the sides of a triangle identify the triangle as acute, right, or obtuse
• If A2 + B2 > C2 then the triangle is an acute triangle
• If A2 + B2 = C2 then the triangle is a right triangle
• If A2 + B2 < C2 then the triangle is an obtuse triangle
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary