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7-4

Similarity in Right Triangles. 7-4. OBJECTIVE. To find and use relationships in right triangles. VOCABULARY. Theorem 7-3 – 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. C.

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7-4

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  1. Similarity in Right Triangles 7-4

  2. OBJECTIVE To find and use relationships in right triangles

  3. VOCABULARY • Theorem 7-3 – 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. C ΔABC~ΔACD~ΔCBD A B D D D A C C B

  4. CLASS WORK Identify the following in right QRS. • the hypotenuse • the segments of the hypotenuse • the altitude • the segment of the hypotenuse adjacent to leg

  5. CLASS WORK Write a similarity statement relating the three triangles in the diagram.

  6. CLASS WORK Use the figure to complete each proportion.

  7. VOCABULARY • Geometric mean – For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that: a x x b • The positive numbers are the extremes, and x represents both means to show that the means are equal.

  8. VOCABULARY • Corollary 1 to Theorem 7-3 – The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. SLLL SLLL AD CD CD DB C LL SL A B D SL LL

  9. VOCABULARY • Corollary 2 to Theorem 7-3 – Each leg of the original (largest) triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg. SLHYP AD AC SLHYP AC AB LLHYP DB CB LL HYP CB AB C HYP HYP LL SL A B D SL LL HYP

  10. CLASS WORK Find the geometric mean of the pair of numbers. Solve for the values of the variables. • 14 and 6

  11. CLASS WORK Find the geometric mean of the pair of numbers. Solve for the values of the variables. • 5 and 25

  12. CLASS WORK The diagram shows the parts of a right triangle with an altitude to the hypotenuse. For the two given measures, find the other four. Use simplest radical form. • h = 12, h1 = 4

  13. EXIT PROBLEMS • Find the geometric mean of 9 and 18. • Solve for the value of the variables.

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

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