Geometry: Special Right Triangles

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.