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

Objectives. Justify and apply properties of 45°-45°-90° triangles. Justify and apply properties of 30°- 60°- 90° triangles.

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

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  1. Objectives Justify and apply properties of 45°-45°-90° triangles. Justify and apply properties of 30°- 60°- 90° triangles.

  2. 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.

  3. Example 1A: Finding Side Lengths in a 45°- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form.

  4. Example 1B: Finding Side Lengths in a 45º- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form.

  5. Example 1C Find the value of x. Give your answer in simplest radical form.

  6. A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

  7. 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.

  8. 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.

  9. Example 2C Find the values of x and y. Give your answers in simplest radical form. y = 2(5) y = 10 Simplify.

  10. Check It Out! Example 2D Find the values of x and y. Give your answers in simplest radical form.

  11. 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?

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