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7.4-APPLYING PROPERTIES OF SIMILAR TRIANGLES

7.4-APPLYING PROPERTIES OF SIMILAR TRIANGLES. 2/4/13. Bell Work 2/4. Solve each proportion. 1. 2. 3. 4. AB = 16. QR = 10.5. x = 21. y = 8. Theorem 1. Example 1. Find US. It is given that , so by the Triangle Proportionality Theorem.

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7.4-APPLYING PROPERTIES OF SIMILAR TRIANGLES

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  1. 7.4-APPLYING PROPERTIES OF SIMILAR TRIANGLES 2/4/13

  2. Bell Work 2/4 Solve each proportion. 1.2. 3.4. AB = 16 QR = 10.5 x = 21 y = 8

  3. Theorem 1

  4. Example 1 Find US. It is given that , so by the Triangle Proportionality Theorem. Substitute 14 for RU, 4 for VT, and 10 for RV. US(10) = 56 Cross Products Prop. Divide both sides by 10.

  5. Example 2 Find PN. Use the Triangle Proportionality Theorem. Substitute in the given values. Cross Products Prop. 2PN = 15 Divide both sides by 2. PN = 7.5

  6. Theorem 2

  7. Example 3 Verify that . Since , by the Converse of the Triangle Proportionality Theorem.

  8. Example 4 AC = 36 cm, and BC = 27 cm. Verify that . Since , then by the Converse of the Triangle Proportionality Theorem.

  9. Corollary 1

  10. Example 5 Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MNto the nearest tenth of an inch.

  11. Example 5 continued AB = 4.5 in. BC = 2.6 in. CD = 4.1 in. KL = 4.9 in. Given 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 2.6 for BC. Cross Products Prop. 4.5(LM) = 4.9(2.6) Divide both sides by 4.5. LM 2.8 in.

  12. Example 5 continued 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 4.1 for CD. 4.5(MN) = 4.9(4.1) Cross Products Prop. MN 4.5 in. Divide both sides by 4.5.

  13. Example 6 Use the diagram to find LM and MN to the nearest tenth. LM 1.5 cm MN 2.4 cm

  14. Theorem 3

  15. Example 7 Find PS and SR. by the ∆ Bisector Theorem. Substitute the given values. Cross Products Property 40(x – 2) = 32(x + 5) Distributive Property 40x – 80 = 32x + 160

  16. Example 7 continued 40x – 80 = 32x + 160 Simplify. 8x = 240 Divide both sides by 8. x = 30 PS = x – 2 SR = x + 5 Substitute 30 for x. = 30 – 2 = 28 = 30 + 5 = 35

  17. Example 8 Find AC and DC. by the ∆ Bisector Theorem. Substitute in given values. Cross Products Theorem 4y = 4.5y – 9 Simplify. –0.5y = –9 Divide both sides by –0.5. y = 18 So DC = 9 and AC = 16.

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