3: Side lengths in a 30-60-90 Triangle Statement: Longer leg = 3 shorter leg 5 = 3 s Reasons: 30-60-90 Triangle Theorem 5 3 3s 3 = 5 s= 5 s= 53 3 s= Substitute values Divide each side by 3 Simplify Multiply numerator and denominator by 3 Simplify 30 60

Because the triangle is a 30- 60-90 triangle, the longer leg is 3 times the length s of the shorter leg. 3: Finding side lengths in a 30- 60-90 Triangle Find the values of s and t. 2: Finding a leg in a 45-45-90 Triangle 5 x x Statement: Hypotenuse = 2 leg 5 = 2 x Reasons: 45-45-90 Triangle Theorem 5 2 2x 2 = 5 x= 5 x= 52 2 x= Substitute values Divide each side by 2 Simplify Multiply numerator and denominator by 2 Simplify The triangle is a 45- 45-90 right triangle, so the length of the hypotenuse is 2 times the length x of a leg. Because the triangle is an isosceles right triangle, its base angles are congruent. 2: Finding a leg in a 45-45-90 Triangle Find the value of x. 1: Finding the hypotenuse in a 45-45-90 Triangle Hypotenuse = 2 leg x = 2 3 x = 32 33 x 45 45-45-90 Triangle Theorem Substitute values Simplify The triangle is a 45-45- 90 right triangle, so the length x of the hypotenuse is 2 times the length of a leg. 1: Finding the hypotenuse in a 45-45-90 Triangle Find the value of x By the Triangle Sum Theorem, the measure of the third angle is 45. 3x 60 30 Hypotenuse = 2 shorter leg Longer leg = 3 shorter leg Theorem 9.8: 30 -60-90 Triangle Theorem In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is 3 times as long as the shorter leg.Theorem 9.8: 45 -45-90 Triangle Theorem In a 45-45-90 triangle, the hypotenuse is 2 times as long as each leg.The theorems that describe these relationships of side lengths of each of these special right triangles follow. Side lengths of Special Right Triangles Right triangles whose angle measures are 45-45-90 or 30- 60-90 are called special right triangles.Assignment: pp.554-555 #1-30 Assignment due to day: 9.3 Quiz Monday over 9.1-9.3 Use special right triangles to solve real-life problems, such as finding the side lengths of the triangles. Objectives/Assignment Find the side lengths of special right triangles.9.4 Special Right Triangles Geometry Mrs.

Special right triangles quiz