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Understanding 45°-45°-90° Triangle Properties and Calculations

This lesson focuses on the properties and theorem of 45°-45°-90° triangles. According to Theorem 7-8, in a 45°-45°-90° triangle, the lengths of both legs are equal, and the length of the hypotenuse is √2 times the length of a leg (Hypotenuse = √2 * leg). Through multiple examples, this lesson illustrates how to find the hypotenuse and leg lengths using provided values, enhancing understanding of this essential geometric principle. Practice problems are included for further mastery.

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Understanding 45°-45°-90° Triangle Properties and Calculations

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Presentation Transcript

  1. Chapter 7 Lesson 3 Objective: To use the properties of 45°-45°-90° triangles.

  2. Theorem 7-8:45°-45°-90° Triangle Theorem In a 45°-45°-90° triangle, both legs are congruent and the length of the hypotenuse is √2 times the length of a leg. Hypotenuse = √2•leg 45° hypotenuse leg 45° leg 45° x√2 x 45° x

  3. 45° 45° 45° 45° Example 1:Finding the Length of the Hypotenuse Find the value of each variable. a. b. 9 2√2 x h h=√2•9 h=9√2 x=√2•2√2 x=4

  4. 45° 45° Example 2:Finding the Length of the Hypotenuse Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 5√3. 5√3 5√3 x=√2•5√3 x=5√6 x

  5. 45° 45° Example 3:Finding the Length of the Hypotenuse Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 5√6. 5√6 5√6 x=√2•5√6 x=5√12 x=5√(4•3) x=10√3 x

  6. 45° 45° Example 4:Finding the Length of a Leg Find the value of x. 6=√2•x 6 x

  7. 45° 45° Example 5:Finding the Length of a Leg Find the length of a leg of a 45°-45°-90° triangle with a hypotenuse of length 10. 10=√2•x 10 x

  8. 45° 45° Example 6:Finding the Length of a Leg Find the length of a leg of a 45°-45°-90° triangle with a hypotenuse of length 22. 22=√2•x 22 x

  9. Assignment Page 369 – 371 #1-9

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