1. Find the length of a segment
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 RQ QU RS ST =
Triangle Proportionality Theorem RQ 9 4 6 =
Substitute.
RQ = 6
Multiply each side by 9 and simplify.

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. CD DE 44 25 = CB BA 27 33 = 9 11

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 .
315 11
ANSWER
2. Determine whether PS || QR .
ANSWER
parallel