In the given figure, l || m and M is the midpoint of AB. Prove that M is also the midpoint of any line segment CD having its end points at l and m respectively.

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Solution

Consider the triangles AMC and BMD.
Since lines l and m are parallel, we have:
$∠ A C D = ∠ M D B (Alternative angles)$
$∠ A M C = ∠ B M D (Vertically opposite angles)$
It is also given that AM = MB.

$∆ A M C ≅ ∆ B M D$ (AAS criterion)
i.e., DM = MC (CPCT)
∴ M is the mid point of segment CD.
Hence, proved.

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In the given figure, l || m and M is the midpoint of AB. Prove that M is also the midpoint of any line segment CD having its end points at l and m respectively.

Consider the triangles AMC and BMD. Since lines l and m are parallel, we have: ∠ACD=∠MDB (Alternative angles) ∠AMC=∠BMD (Vertically opposite angles) It is also given that AM = MB. ∆AMC≅∆BMD (AAS criterion) i.e., DM = MC (CPCT) ∴ M is the mid point of segment CD. Hence, proved.