Lesson 8 – 3 Special Right Triangles

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Presentation transcript:

Lesson 8 – 3 Special Right Triangles Geometry Lesson 8 – 3 Special Right Triangles Objective: Use the properties of 45-45-90 triangles. Use the properties of 30-60-90 triangles.

45-45-90 triangle Find the hypotenuse for the following: 12 + 12 = x2

45-45-90 Triangle Theorem In a 45-45-90 degree triangle, the legs l are congruent and the length of the hypotenuse h is times the length of the leg.

little different, be careful. Find x 6 Same concept, but a little different, be careful. Use this setup. x = 9(2) x = 18

Find x. x = 14

Find x. Same concept, only solving in different order. Don’t forget to simplify the radical!

Find x. 5 = x

14 20 7 10 72 + b2 = 142 102 + b2 = 202 b2 = 147

30-60-90 Triangle Since 30 is x. 60 is 2(30). So 60 is 2x. 2x 2x How can we find the length of a?

30-60-90 Triangle Theorem In a 30-60-90 triangle, the length of the hypotenuse h is 2 times the length of the shorter leg s, and the length of the longer leg is l is times the length of the shorter leg.

Find x and y. 2x 30 So y = 2x

Find x & y. 2x

Find x & y 2x = 10 x = 5 2x

Find x & y x = 2(21) = 42 2x x

Find x & y x 2x x = 4

Homework Pg. 556 1 – 7 all, 8 – 32 EOE, 38, 48, 52 – 64 E