9.7 Special Right Triangles Objective: After studying this section, you will be able to identify the ratio of side lengths in a 30°-60°-90° triangle and in a 45°-45°-90° triangle.

Theorem In a triangle whose angles have the measures 30°, 60°, and 90°, the lengths of the sides opposite these angles can be represented by a,, and 2a respectively. (30°-60°-90° Triangle Theorem) 30° 60° a 2a NOTE: This information can also be found on your AIMS Reference Sheet!

Given: Triangle ABC is equilateral Prove: The ratio of AD:DC:AC = (Hint: use a paragraph proof!) A C BD 60° 30° 2a a And now…for the moment of Proof!

Theorem In a triangle whose angles have the measures 45°, 45°, and 90°, the lengths of the sides opposite these angles can be represented by a, a, and respectively. (45°-45°-90° Triangle Theorem) 45° a a

Example 1: Find BC and AC Example 2: Find JK and HK 60° 106 A B CJ K H

Example 3: MOPR is a square. Find MP Example 4: Find ST and TV 45° 9 4 M P O R S T V Last 2 practice problems…

Summary… State how to classify triangles. Explain in your own words the Pythagorean Theorem. Classwork… Break up into groups of 3 or 4. All groups will be given a special right triangle problem and a designated whiteboard. Once the group has solved for the missing sides, 1 representative will hold up the group’s whiteboard. The group with the most points will be dubbed Special Right Triangles Royalty!

Homework Worksheet 9.7 Special Right Triangles Parts 1 and 2!