Section 5.5: Special Right Triangles

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Presentation transcript:

Section 5.5: Special Right Triangles Theorem 5.5.1 (45-45-90 Theorem) In a triangle whose angles measure 45, 45 and 90, the hypotenuse has a length equal to the product of 2 and the length of either leg. Ex.1 p.250 Theorem 5.5.2(30-60-90 Theorem) In a triangle whose angles measure 30, 60 and 90, the hypotenuse has a length equal to twice the length of the shorter leg, and the length of the longer leg is the product of 3 and the length of the shorter leg. Proof p. 251 11/24/2018 Section 5.5 Nack

The Converse Theorems Theorem 5.5.3: If the length of the hypotenuse of a right triangle equals the product of 2 and the length of either leg, then the angles of the triangle measure 45, 45 and 90. Theorem 5.5.4:If the length of the hypotenuse of a right triangle is twice the length of one leg of the triangle, then the angle of the triangle opposite that leg measures 30. Ex. 4, 5,6 p. 252-254 11/24/2018 Section 5.5 Nack