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Chapter 7 Section 4 Similarity in Right Triang les

Chapter 7 Section 4 Similarity in Right Triang les. Objectives . Students will be able to find and use relationships within right triangles. Essential Understanding. When you draw the altitude to the hypotenuse of a right triangle you form three pairs of similar triangles. Theorem.

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Chapter 7 Section 4 Similarity in Right Triang les

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  1. Chapter 7 Section 4 Similarity in Right Triangles

  2. Objectives Students will be able to find and use relationships within right triangles

  3. Essential Understanding When you draw the altitude to the hypotenuse of a right triangle you form three pairs of similar triangles

  4. Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

  5. What similarity statement can you write relating the three triangles?

  6. Geometric Mean Proportions in which the means are equal For numbers a and b, the geometric mean is the positive number x such that: a = xxb Then you cross multiply and solve for x

  7. Find the Geometric Mean Geometric mean of 6 and 15 Geometric mean of 4 and 18 Geometric mean of 5 and 12

  8. From the first example

  9. Theorem The length of an altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

  10. Theorem The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the hypotenuses and the length of the segment of the hypotenuses adjacent to the leg

  11. Example

  12. What are the values of x and y?

  13. What are the values of x and y?

  14. What are the values of x and y?

  15. Homework Pg. 465 # 9 – 23, 31, 38 – 41 20 problems

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