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Corollary 1 to Theorem 7-3• Corollary The length of the altitude to the If… C hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. A D B Then…Example 2 AD = CD CD DB 8 Segments of 2 4 Altitude to 4 hypotenuse = hypotenuse 4 8
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Corollary 2 to Theorem 7-3• Corollary The altitude to the hypotenuse of a right triangle separates the hypotenuse If… C so that the length of each leg of the triangle is the geometric mean of the length of the hypotenuse and the length A D B of the segment of the hypotenuse adjacent to the leg. Then… Example AB = AC and AB = CB AC AD CB DB 1 4 Hypotenuse 4 2 Leg = 2 2 1 Segment of hypotenuse adjacent to leg
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Find the geometric mean for each pair of numbers.1. 4 and 9 2. 3 and 18 3. 5 and 9 6 ≈7.3 ≈6.74. 9 and 16 5. 5 and 80 6. 8 and 32 12 20 16Find the value of the variables.13. 8. x≈8.4 x≈2.2 y≈4.6 y=2 z≈5.5 z≈4.59. 10. x=65 x=6 y=60 y≈4.5 z=156 z≈6.7
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LEARNING GOALS SCALE - Unit 7-4: Similarity in Right Triangles •Students will be able to identify corresponding parts of similar right triangles. •Students will understand and be able to understand Theorem 7-3 and its corollaries. SCORE LEARNING GOALS ACHIEVED “I CAN TEACH IT!”4 •I am able to identify similar right triangles. •I understand and can use Theorem 7-3. •I understand and can use the Corollaries to Theorem 7-3. •I answered all practice questions correctly. •I am able to help other students achieve the learning goals. “GOT IT…Yes!”3 •I am able to identify similar right triangles. •I understand or can use Theorem 7-3. •I understand or can use the Corollaries to Theorem 7-3. •I answered 8 or 9 practice questions correctly. “ALMOST! Yes, but…”2 •I am able to identify similar right triangles. •I understand Theorem 7-3. •I understand the Corollaries to Theorem 7-3. •I answered 6 or 7 practice questions correctly. “GETTING THERE….No, but…”1 •I am able to identify similar right triangles. •I answered 5 practice questions correctly. “CLUELESS… No idea”0 •I have NO idea what you are talking about. •“WHAT????” •I answered fewer than 5 practice questions correctly.
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