Question

State true or false.

In the figure, $l||m$ and M is the midpoint of line segment $AB$. Then $M$ is also the midpoint of any line segment having its endpoints $C$ and $D$ on $l$ and $m$ respectively.

• A. True
• B. False

Answer 1

The correct option is A True

$AM=MB\angle DMB=\angle AMC\left(VerticallyOppositeAngle\right)\angle ACD=\angle CDB\left(AlternatingAngle\right)$

Hence, According to ASA Congruency Criterion

$△AMC\cong △DMB$

Hence, $DM=MC$

So, Point M is mid-point of CD