Question

For the following figure, given that $TA=TB=BC$and $TD=DE=EF$.

Tony makes up a problem for the figure, setting $AD=5$and $CF=17$. Katie says, “You can’t do that.” Explain.

Short answer

The figure is not possible.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

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:

$\begin{array}{l}BE=\frac{AD+CF}{2}\\ BE=\frac{5+17}{2}\\ BE=11\end{array}$

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.