5 8 Applying Special Right Triangles Objectives Justify
5 -8 Applying Special Right Triangles Objectives Justify and apply properties of 45°-90° triangles. Justify and apply properties of 30°- 60°- 90° triangles. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles A diagonal of a square divides it into two congruent isosceles right triangles. Since the base angles of an isosceles triangle are congruent, the measure of each acute angle is 45°. So another name for an isosceles right triangle is a ______ triangle. A 45°-90° triangle is one type of special right triangle. You can use the Pythagorean Theorem to find a relationship among the side lengths of a 45°-90° triangle. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 1 A: Finding Side Lengths in a 45°- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 1 B: Finding Side Lengths in a 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 1 C Find the value of x. Give your answer in simplest radical form. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 2 A: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. 22 = 2 x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 2 B: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. Rationalize the denominator. y = 2 x Hypotenuse = 2(shorter leg). Simplify. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 2 C Find the values of x and y. Give your answers in simplest radical form. y = 2(5) y = 10 Simplify. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Check It Out! Example 2 D Find the values of x and y. Give your answers in simplest radical form. Holt Mc. Dougal Geometry
5 -8 Applying Special Right Triangles Example 4: Using the 30º-60º-90º Triangle Theorem An ornamental pin is in the shape of an equilateral triangle. The length of each side is 6 centimeters. Josh will attach the fastener to the back along AB. Will the fastener fit if it is 4 centimeters long? Holt Mc. Dougal Geometry
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