Question

In figure $M$ is the mid-point of both $AC$ and $BD$. Then

• A. $\angle 1=\angle 2$
• B. $\angle 1=\angle 4$
• C. $\angle 2=\angle 4$
• D. $\angle 1=\angle 3$

Answer 1

The correct option is B

$\angle 1=\angle 4$

Estimate the Equal Angles:

In $△AMB$and $△CMD$

$AM=CM$ {M is mid point of AC, hence $M$ divides $AC$ into two equal parts}

$BM=DM$ {M is mid point of BD, hence $M$ divides $BD$ into two equal parts}

$\angle AMB=\angle CMD$ {vertically opposite angle}

Vertically opposite angles are the angles that are opposite to each other in a pair of intersecting lines.

Therefore by SAS criterion

$$\begin{gathered} \therefore △AMB\cong △CMD \\ \therefore \angle 1=\angle 4 \end{gathered}$$

Hence, option (B) is correct