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Proportional Lengths and Parallel Lines in Diagrams

This text explains the use of the Triangle Proportionality Theorem and the concept of parallel lines in solving length-related problems in diagrams. It also provides guided practice for further understanding.

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Proportional Lengths and Parallel Lines in Diagrams

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  1. In the diagram, QS || UT , RS = 4, ST = 6, and QU = 9. What is the length of RQ ? RQ RS = QU ST RQ 4 = 9 6 EXAMPLE 1 Find the length of a segment SOLUTION Triangle Proportionality Theorem Substitute. RQ = 6 Multiply each side by 9 and simplify.

  2. On the shoerack shown,AB = 33 cm, BC = 27 cm, CD = 44 cm,and DE = 25 cm, Explain why the gray shelf is not parallel to the floor. CB 27 9 CD 44 = = = BA 33 11 DE 25 EXAMPLE 2 Solve a real-world problem Shoerack SOLUTION Find and simplify the ratios of lengths determined by the shoerack.

  3. ANSWER 44 9 Because , BDis not parallel to AE. So, the shelf is not parallel to the floor. = 25 11 EXAMPLE 2 Solve a real-world problem

  4. 1. Find the length of YZ . XW XY = YZ WV 44 36 = 35 YZ 315 YZ = 11 315 So length of YZ = ANSWER 11 for Examples 1 and 2 GUIDED PRACTICE SOLUTION Triangle Proportionality Theorem Substitute. Simplify

  5. 2.Determine whetherPS || QR . 5 PQ RS 50 5 40 = = = = SN 9 PN 90 9 72 PQ RS = SN PN ANSWER PS || QR , So Because = PS is parallel to QR for Examples 1 and 2 GUIDED PRACTICE SOLUTION

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