Question

In the following figure, l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.

Answer 1

Given: In the following figure, l || m and M is the mid-point of a line segment AB i.e., AM = BM.

To show: MC = MD

Proof: l || m  ...[Given]

∠BAC = ∠ABD   ...[Alternate interior angles]

∠AMC = ∠BMD   ...[Vertically opposite angles]

In ΔAMC and ΔBMD,  

∠BAC = ∠ABD  ...[Proved above]

AM = BM   ...[Given]

And ∠AMC = ∠BMD   ...[Proved above]

∴ ΔAMC ≅ ΔBMD   ...[By ASA congruence rule]

⇒ MC = MD   ...[By CPCT]