Use Similar Right Triangles

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8-1 Similarity in Right Triangles

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Presentation transcript:

Use Similar Right Triangles Geometry Section 7.3 Use Similar Right Triangles

Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

Examples Identify the similar triangles then find the value of x. L B 13 K 5 12 D 3 x x J A A C 5 5 4 M

Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments.

Geometric Mean (Leg) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

Examples Find the length of the variable using the geometric mean theorems. 8 5 8 x 4 y 5

Assignment Section 7.3 Page 453 Problems #4-24 even