Question

Given that $▱ABCD$ and M is the midpoint of $\overline{AB}$. Then prove that $MO=\frac{1}{2}AD$.

Short answer

The statement is $MO=\frac{1}{2}AD$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Consider that the two triangles $\Delta MOB,\Delta ADB$.

Here $\angle B$is common in both the angles such that $\angle MBO=\angle ABD$.

Since M is the midpoint of AB such that $\frac{MB}{AB}=\frac{1}{2}$.

From the figure, the diagonals of the parallelogram intersect each other as $\frac{OB}{DB}=\frac{1}{2}$.

Step 3. Step description.

By the SAS postulates, it is clear that $\Delta MOB~\Delta ADB$.

Since $\frac{MO}{AD}=\frac{1}{2}$thus $MO=\frac{1}{2}AD$

Therefore, $MO=\frac{1}{2}AD$.