Special Right Triangles

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Presentation transcript:

Special Right Triangles Obj: To use the properties of 45-45-90 and 30-60-90 right triangles

Theorem In a 45-45-90 triangle, the hypotenuse is the square root of 2 times as long as the leg. 4

Example 8 cm Find a. The length of the hypotenuse of a 45°-45°-90° triangle is times as long as a leg of the triangle. Answer:

Theorem In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is the square root of 3 times as long as the shorter leg. 2x x

Example Find QR. is the longer leg, is the shorter leg, and is the hypotenuse. Answer:

Your Turn Find BC. 4 = AB So BC = 2AB So BC = 8 Answer: BC = 8 in.

Point W has the same x-coordinate as X. W is located units below X. COORDINATE GEOMETRY is a 30°-60°-90° triangle with right angle X and as the longer leg. Graph points X(-2, 7) and Y(-7, 7), and locate point W in Quadrant III. is the shorter leg. is the longer leg. So, Use XY to find WX. Point W has the same x-coordinate as X. W is located units below X. Answer: The coordinates of W are or about

Put this in your agenda Pg 461 3-11 odd, 13 - 18, 20 - 21, 23 - 28 Homework