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8.4: Similarity in Right Triangles

8.4: Similarity in Right Triangles. Objectives: Students will be able to… Find the geometric mean between 2 numbers Find and use relationships between similar right triangles. Geometric Mean:. In a proportion, , b and c are called the “means”

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8.4: Similarity in Right Triangles

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  1. 8.4: Similarity in Right Triangles Objectives: Students will be able to… Find the geometric mean between 2 numbers Find and use relationships between similar right triangles.

  2. Geometric Mean: • In a proportion, , b and c are called the “means” • Proportions in which the means are = occur frequently in geometry. THE GEOMETRIC MEAN, x:

  3. Find the Geometric Mean of the following numbers: • 2 and 10 • 25 and 4 • 15 and 3

  4. Definition: ALTITUDE of a triangle The altitude is a segment from a vertex of a triangle that is perpendicular to the opposite side (or the line containing the opposite side).

  5. In a right triangle, the altitude to the hypotenuse creates 3 similar triangles. C C B A D B A D B

  6. Right Triangle Similarity LEG B LEG A ALTITUDE D C HYPOTENUSE PROPORTIONS WHERE ALTITUDE AND LEGS ARE GEOMETRIC MEANS:

  7. The length of the altitude of a right triangle is the geometric mean of the 2 pieces (segments) of the hypotenuse ALTITUDE D C Example: Find x. x 12 3

  8. Examples: Find x. 1. 2. 3. 2 8 x 3 9 x x 40 50

  9. The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the leg is geometric mean of length of adjacent piece of hypotenuse and the whole length of hypotenuse. LEG B LEG A ALTITUDE D C Example: Find x. x 4 16

  10. Examples. Find the value of x. 1. 2. 3. x 4 5 x 6 20 36 x 60

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