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Question
In the following figure, M is the mid-point of both AC and BD. Then ______.
Options
∠1 = ∠2
∠1 = ∠4
∠2 = ∠4
∠1 = ∠3
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Solution
In the following figure, M is the mid-point of both AC and BD. Then ∠1 = ∠4.
Explanation:
In ΔAMB and ΔCMD,
AM = CM ...[M is the mid-point]
BM = DM ...[M is the mid-point]
∠AMB = ∠CMD ...[Vertically opposite angles]
By SAS congruence criterion,
ΔAMB ≅ ΔCMD
∴ ∠1 = ∠4 ...[By C.P.C.T]
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