Question

In Exercises 12-20, $\mathrm{TA}=\mathrm{AB}=\mathrm{BC}$and $\mathrm{TD}=\mathrm{DE}=\mathrm{EF}$

Write an equation that relates AD and BE. (Hint: Think of $\Delta \mathrm{TBE}$)

Short answer

The equation that relates AD and BE is $\mathrm{BE}=2\mathrm{AD}$.

Step-by-step solution

Step 1. Highlight Triangle ABE in the given figure.

Step 2. Description of step.

Consider $\Delta TBE$. From the figure, it can be observed that $TA=AB\text{and}TD=DE$.

Step 3. Description of step.

From the figure, it can be observed that AD is the midsegment of $\Delta TBE$. The midsegment theorem states that the length of the midsegment is half of the base of the triangle. Therefore,

$\begin{array}{c}AD=\frac{BE}{2}\\ BE=2AD\end{array}$

Therefore, an equation that relates AD and BE is $BE=2AD$.