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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, a 3 , and 2a respectively. (30°-60°-90° Triangle Theorem) 60° 2a a 30° a 3 NOTE: This information can also be found on your AIMS Reference Sheet! And now…for the moment of Proof! C Given: Triangle ABC is equilateral 30° CD bisects ACB 2a Prove: The ratio of AD:DC:AC = a : a 3 : 2a 60° A (Hint: use a paragraph proof!) a D B 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 a 2 respectively. (45°-45°-90° Triangle Theorem) 45° a 2 a 45° a Example 1: Example 2: Find BC and AC Find JK and HK H A 10 6 60° B C K 60° J Last 2 practice problems… Example 3: Example 4: MOPR is a square. Find ST and TV T Find MP M R V 9 O P 45° 4 S 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!