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Justify and apply properties of 45°-45°-90° triangles.

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##### Justify and apply properties of 45°-45°-90° triangles.

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**Objectives**Justify and apply properties of 45°-45°-90° triangles. Justify and apply properties of 30°- 60°- 90° 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°-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°-45°-90° triangle.**Example 1A: Finding Side Lengths in a 45°- 45º- 90º**Triangle Find the value of x. Give your answer in simplest radical form.**Example 1B: Finding Side Lengths in a 45º- 45º- 90º**Triangle Find the value of x. Give your answer in simplest radical form.**Example 1C**Find the value of x. Give your answer in simplest radical form.**A 30°-60°-90° triangle is another special right triangle.**You can use an equilateral triangle to find a relationship between its side lengths.**Example 2A: Finding Side Lengths in a 30º-60º-90º**Triangle Find the values of x and y. Give your answers in simplest radical form. 22 = 2x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x.**Example 2B: 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 = 2x Hypotenuse = 2(shorter leg). Simplify.**Example 2C**Find the values of x and y. Give your answers in simplest radical form. y = 2(5) y = 10 Simplify.**Check It Out! Example 2D**Find the values of x and y. Give your answers in simplest radical form.**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?