Question

In the given figure, $l\parallel m$ and $M$ is the mid-point of the line segment $AB.$ Which of the following options is/are correct?

• A. $CM=DM$
• B. $DM=BM$
• C. $AM=CM$
• D. None of these

Answer 1

The correct option is A

$CM=DM$

In $\Delta AMC$ and $\Delta BMD$, we have
$\begin{array}{cc}\angle 1=\angle 3& \left[\text{alternate opposite angles}\right]\\ \angle 2=\angle 4& \left[\text{vertically opposite angles}\right]\\ AM=BM& \left[\text{given M is the mid-point of AB}\right]\end{array}$
$\therefore \Delta AMC\cong \Delta BMD$ [by $ASA$ congruence rule]
$\therefore CM=DM$ [CPCT]
Hence, $M$ is also the mid-point of $CD.$