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Geometry Section 7.3

Geometry Section 7.3. Use Similar Right Triangles. 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. Theorem. Examples. Identify the similar triangles then find the value of x. L. B. 13. K.

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Geometry Section 7.3

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  1. GeometrySection 7.3 Use Similar Right Triangles

  2. 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. Theorem

  3. 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 M 4

  4. 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 (Altitude) Theorem

  5. 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. Geometric Mean (Leg) Theorem

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

  7. Assignment • Section 7.3 • Page 453 • Problems #4-24 even

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