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Chapter 5: Q13 (page 193)

In Exercises 12-20, TA=AB=BCand TD=DE=EF

Write an equation that relates AD,BEand CF. (Hint: Think of trapezoid CFDA).

Short Answer

Expert verified

The equation that relates AD, BEand CF is 2BE=AD+CF.

Step by step solution

01

Step 1. Highlight a trapezoid in the given figure.

02

Step 2. Description of step.

Consider a trapezoid CFDA. From the figure, it can be observed that BC=ABandEF=DE.

03

Step 3. Description of step.

From the figure, it can be observed that BE is the median of trapezoid CFDA. According to the property of the median of a trapezoid, the length of the median is the average of the two base lengths. Therefore,

BE=12AD+CF2BE=AD+CF

Therefore, the equation that relates AD, BEand CF is 2BE=AD+CF.

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