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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. In the figure below, if RS // VT, then find y. 9.0 6.75 4.8 7.6 3.6 5.7 K L J G H I 4.5 12 9 3.5 A B C D E ∆BAC ~ ∆DEC AA Similarity No. Sides are not proportional ∆GHI ~ ∆KLJ SSS Similarity Standardized Test Practice: R S V U T 5 3 8 y + 12 A -0.8 B B 0.8 C 1.2 D 4.8 Click the mouse button or press the Space Bar to display the answers.
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Parallel Lines and Proportional Parts
Lesson 6-4 Parallel Lines and Proportional Parts
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Objectives Use proportional parts of triangle
Divide a segment into parts
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Vocabulary Midsegment: a segment whose endpoints are the midpoints of two sides of the triangle
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Example 1a S 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. Answer:
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Example 1b B In ∆ABC, AC // XY, AX=4, XB=10.5 and CY=6. Find BY.
Answer:
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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 Since the sides have proportional length. Answer: since the segments have proportional lengths,
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Example 2b In ∆WXZ, XY=15, YZ=25, WA=18 and AZ=32. Determine whether WX // AY. Explain. X Answer: No; the segments are not in proportion since
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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
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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
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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
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Example 4b Find a and b. Answer: a = 11; b = 1.5
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Summary & Homework Summary: Homework:
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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