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5-Minute Check on Lesson 6-3

Transparency 6-4. 5-Minute Check on Lesson 6-3. Determine if each pairs of triangles are similar. If so, write a similarity statement. Justify your statement. 2. 3.

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5-Minute Check on Lesson 6-3

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  1. Transparency 6-4 5-Minute Check on Lesson 6-3 • Determine if each pairs of triangles are similar. If so, write a similarity statement. Justify your statement. • 2. 3. • 4. In the figure below, if RS // VT, then find y. D E C 9 H 6.75 A B K J 7.6 3.5 4.8 ∆BAC ~ ∆DECAA Similarity 3.6 ∆GHI ~ ∆KLJ SSS Similarity No. Sides are notproportional 5.7 4.5 I G L 9.0 12 Standardized Test Practice: S R T 3 y + 12 V 8 5 U B A B C D 4.8 -0.8 0.8 1.2 Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 6-4 Parallel Lines and Proportional Parts

  3. Objectives • Use proportional parts of triangle • Divide a segment into parts

  4. Vocabulary • Midsegment: a segment whose endpoints are the midpoints of two sides of the triangle

  5. S Answer: Example 1a In ∆RST, RT // VU, SV = 3, VR = 8, and UT = 12. Find SU. From the Triangle Proportionality Theorem, Multiply. Divide each side by 8. Simplify.

  6. B Example 1b In ∆ABC, AC // XY, AX=4, XB=10.5 and CY=6. Find BY. Answer: 15.75

  7. Since the sides have proportional length. Answer: since the segments have proportional lengths, Example 2a In ∆DEF, DH=18, HE=36, and 2DG = GF. Determine whether GH // FE. Explain. In order to show that we must show that

  8. X Answer: No; the segments are not in proportion since Example 2b In ∆WXZ, XY=15, YZ=25, WA=18 and AZ=32. Determine whether WX // AY. Explain.

  9. Example 3 In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Triangle Proportionality Theorem Multiply. Divide each side by 13. Answer: 32

  10. Example 3b In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Answer: 5

  11. Example 4a Find x and y. To find x: Given Subtract 2x from each side. Add 4 to each side. To find y:The segments with lengths 5y and (8/3)y + 7 are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal. Equal lengths Multiply each side by 3 to eliminate the denominator. Subtract 8y from each side. Divide each side by 7. Answer: x = 6; y = 3

  12. Example 4b Find a and b. Answer: a = 11; b = 1.5

  13. Summary & Homework • Summary: • A segment that intersects two sides of a triangle and is parallel to the third side divides the two intersected sides in proportion • If two lines divide two segments in proportion, then the lines are parallel • Homework: • Day 1: pg 311-2: 9,10, 14-18 • Day 2: pg 312-3: 11, 12, 20, 21, 23-26, 33, 34

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