Chapter 7 Lesson 3

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

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

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

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

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

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

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

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

Assignment Page 369 – 371 #1-9

Chapter 7 Lesson 3