# 10.4.1. Parallel Lines and Proportional Parts

Given that cm, cm, cm, cm, and cm, find the lengths of and .

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm

### Example

Given that cm, cm, cm, cm, and cm, find the lengths of and .

### Solution

In and , corresponds to , corresponds to , and corresponds to . Also, side corresponds to side , side corresponds to side , and side corresponds to side . and are parallel line segments cut by transversals and .

If a line segment is drawn parallel to one side of a triangle and intersects the other two sides, then it divides the other two sides into segments whose lengths are proportional. Now use this fact, along with the fact that , to write another equation in the variables and .

Since and , it must be true that . Solve this equation for as follows:

Now solve either the equation or the equation for .

Since , calculate the length of as follows.

Next, calculate the length of .

Thus, the length of is cm, and the length of is cm.

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