1. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles 7-4 Applying Properties of Similar Triangles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

2. 7-4 Applying Properties of Similar Triangles Warm Up Solve each proportion. 1. 2. 3. 4. AB = 16QR = 10.5 x = 21y = 8

3. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems. Objectives

4. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles (The pieces are proportional) (Top/Bottom=Top/Bottom)

5. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 1: Finding the Length of a Segment Find US. Substitute 14 for RU, 4 for VT, and 10 for RV. Cross Products Prop. US(10) = 56 Divide both sides by 10. It is given that, so by the Triangle Proportionality Theorem. COPY THIS SLIDE:

6. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 1 Find PN. Substitute in the given values. Cross Products Prop. 2PN = 15 PN = 7.5Divide both sides by 2. Use the Triangle Proportionality Theorem. COPY THIS SLIDE:

7. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles COPY THIS SLIDE: (If the pieces are proportional, then the line is parallel.)

8. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 2: Verifying Segments are Parallel Verify that. Since,. COPY THIS SLIDE:

9. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that. Since,. COPY THIS SLIDE:

10. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles COPY THIS SLIDE: This is the same thing, but without a triangle: Top/Bottom=Top/Bottom

11. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 3: Art Application 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 MN to the nearest tenth of an inch. COPY THIS SLIDE:

12. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 3 Continued 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.

13. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 3 Continued 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 4.1 for CD. Cross Products Prop.4.5(MN) = 4.9(4.1) Divide both sides by 4.5. MN  4.5 in.

14. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 3 Use the diagram to find LM and MN to the nearest tenth.

15. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Given Check It Out! Example 3 Continued 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 1.4 for BC. Cross Products Prop.2.4(LM) = 1.4(2.6) Divide both sides by 2.4. LM  1.5 cm

16. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 3 Continued 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 2.2 for CD. Cross Products Prop.2.4(MN) = 2.2(2.6) Divide both sides by 2.4. MN  2.4 cm

17. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles The previous theorems and corollary lead to the following conclusion. COPY THIS SLIDE: (Left/Right=Left/Right)

18. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 4: Using the Triangle Angle Bisector Theorem Find PS and SR. Substitute the given values. Cross Products Property Distributive Property by the ∆  Bisector Theorem. 40(x – 2) = 32(x + 5) 40x – 80 = 32x + 160 COPY THIS SLIDE:

19. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Example 4 Continued Simplify. Divide both sides by 8. Substitute 30 for x. 40x – 80 = 32x + 160 8x = 240 x = 30 PS = x – 2SR = x + 5 = 30 – 2 = 28= 30 + 5 = 35

20. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Check It Out! Example 4 Find AC and DC. Substitute in given values. Cross Products Theorem So DC = 9 and AC = 16. Simplify. by the ∆  Bisector Theorem. 4y = 4.5y – 9 –0.5y = –9 Divide both sides by –0.5.y = 18

21. Holt McDougal Geometry 7-4 Applying Properties of Similar Triangles Classwork/Homework: 7.4 #’s:1-14all