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Chapter 5: Q19 (page 193)

For the following figure, given that TA=TB=BCand TD=DE=EF.

Tony makes up a problem for the figure, setting AD=5and CF=17. Katie says, 鈥淵ou can鈥檛 do that.鈥� Explain.

Short Answer

Expert verified

The figure is not possible.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

Consider that TA=AB=BC,TD=DE=EF,AD=5,CF=17.

Use the mid-segment or median of the trapezoid as follows:

BE=AD+CF2BE=5+172BE=11

03

Step 3. Step description.

AD should be half of BE, but here AD=5, so the figure is not possible.

Therefore, the figure is not possible.

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