8-3 Special Right Triangles You used properties of isosceles and equilateral triangles. Use the properties of 45°-45°-90° triangles. Use the properties of 30°-60°-90° triangles.

Making of an Isosceles Right Triangle #1 How can you make an isosceles right triangle?

Right Ratios Use the Pythagorean Theorem to find the third side. 45°

45°- 45°- 90° Right Triangle In a 45°- 45°- 90° triangle, the hypotenuse is √2 times as long as either leg. The ratios of the side lengths can be written l-l-l√2. l l p. 558

Find the length of the side 10 x r s a b 9 r = s = 4

Find x. The given angles of this triangle are 45° and 90°. This makes the third angle 45°, since 180 – 45 – 90 = 45. Thus, the triangle is a 45°-45°-90° triangle. Substitution 45°-45°-90° Triangle Theorem

Find x. The legs of this right triangle have the same measure, x, so it is a 45°-45°-90° triangle. Use the 45°-45°-90° Triangle Theorem. Substitution 45°-45°-90° Triangle Theorem x = 12 Answer: x = 12

Find x. A.3.5 B.7 C. D.

Find x. A. B. C.16 D.32

Find a. The length of the hypotenuse of a 45°-45°-90° triangle is times as long as a leg of the triangle. Substitution 45°-45°-90° Triangle Theorem Multiply. Divide. Rationalize the denominator. Divide each side by

Making of an Isosceles Right Triangle #2 How can you make an isosceles right triangle? 60°

Right Ratios Use the Pythagorean Theorem to find the third side ? 60° 30°

30°- 60° - 90° Right Triangle In a 30°- 60° - 90° triangle, the hypotenuse is twice as long as the shorter leg (the leg opposite the 30° angle, and the longer leg (opposite the 60° angle) is √3 tunes as long as the shorter leg. The ratios of the side lengths can be written l - l√3 – 2l. 60° 30° l 2l p. 560

Find the length of the side 30° 60° 30° 60° 30° 60° 30° 60° l = 8 2l = 20 l = 10 l = 5 2l =

Find BC. A.4 in. B.8 in. C. D.12 in.

BOOKENDS Shaina designed 2 identical bookends according to the diagram below. Use special triangles to find the height of the bookends. A. B.10 C.5 D.

What two type of right triangles occur often? 30°-60°-90° and 45°-45°-90°. How can you find the length of a side of a special right triangle knowing only one side? 60° 30° l 2l l l

8-3 Assignment Worksheet 5-3B Skip 12-14