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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.
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Solution
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]
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