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9.7 Special Right Triangles

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

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9.7 Special Right Triangles

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  1. 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.

  2. 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) 60° 2a a 30° NOTE:This information can also be found on your AIMS Reference Sheet!

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

  4. 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 45° a

  5. Example 2: Find JK and HK Example 1: Find BC and AC H A 10 6 60° 60° C J B K

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

  7. 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!

  8. Homework Worksheet 9.7 Special Right Triangles Parts 1 and 2!

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