Name _______________________________________ Date ___________________ Class __________________ Section 5.8 Applying Special Right Triangles Theorem Example 458-458-908 Triangle Theorem In a 458-458-908 triangle, both legs are congruent and the length of the hypotenuse is 2 times the length of a leg. In a 458-458-908 triangle, if a leg length is x, then the hypotenuse length is x 2. Use the 458-458-908 Triangle Theorem to find the value of x inEFG. Every isosceles right triangle is a 458-458-908 triangle. Triangle EFG is a 458-458-908 triangle with a hypotenuse of length 10. 10 x 2 10 2 x 2 5 2x 2 Hypotenuse is 2 times the length of a leg. Divide both sides by 2. Rationalize the denominator. Find the value of x. Give your answers in simplest radical form. 1. 2. ________________________________________ 3. ________________________________________ 4. ________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Section 5.8 Applying Special Right Triangles continued Theorem Examples 308-608-908 Triangle Theorem In a 308-608-908 triangle, the length of the hypotenuse is 2 multiplied by the length of the shorter leg, and the longer leg is 3 multiplied by the length of the shorter leg. In a 308-608-908 triangle, if the shorter leg length is x, then the hypotenuse length is 2x and the longer leg length is x. Use the 308-608-908 Triangle Theorem to find the values of x and y inHJK. 12 x 3 12 3 x 4 3x Longer leg shorter leg multiplied by Divide both sides by 3. 3. Rationalize the denominator. y 2x Hypotenuse 2 multiplied by shorter leg. y 2(4 3) Substitute 4 3 for x. y 8 3 Simplify. Find the values of x and y. Give your answers in simplest radical form. 5. 6. ________________________________________ 7. ________________________________________ 8. ________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Section 5.8 1. x 17 2 2. x 22 2 3. x 4 2 4. x 25 5. x 9; y 9 3 6. x 2 3 ; y 4 7. x 12 3 ; y 36 8. x 11 3 ; y 22 3 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry