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

2. EXAMPLE 2 Solve a real-world problem 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. Shoerack SOLUTION Find and simplify the ratios of lengths determined by the shoerack. CB BA 27 33 = 9 11 = CD DE 44 25 =

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

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

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