7.4 Special Right Triangles

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Presentation transcript:

7.4 Special Right Triangles Hubarth Geometry

45-45-90 Triangle Theorem Side-angle Correlation 45 x 45 x

Ex 1 Find the Hypotenuse Length Find the length x of the hypotenuse in the 45-45-90 triangle shown at the right. 3 3 45 x Solution

Ex 2 Find Leg Length Find the length x of each leg in the 45-45-90 triangle. 45 x 45 x Solution

45-45-90 Triangle Theorem Substitute. Ex 3 Standardized Test Practice By the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o hypotenuse = leg 2 45-45-90 Triangle Theorem = 25 2 WX Substitute. The correct answer is B.

30-60-90 Triangle Theorem 30 2x 60 x

Ex 4 Find Hypotenuse Length In the 30-60-90 triangle, the length of the shorter leg is given. Find the length of the hypotenuse. 60 12 30 Solution The side opposite the 30 is the shorter leg.

Ex 5 30-60-90 Triangle Find the values of x and y. Write your answer in simplest radical form. STEP 1 Find the value of x. longer leg = shorter leg 3 9 = x 3 9 3 = x STEP 2 Find the value of y. hypotenuse = 2 shorter leg 9 3 = x 𝑦=2∙3 3 =6 3 9 3 = x 3 = x

Practice 2. x x 1. 45 x 4 45 45 8 3. x=14 4. 30 x 30 42 y 60 7 60 x