Question

In the given figure, O is the mid-point of AB and CD Prove that
(a) AAOC ABOD
(b) AC = BD
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Answer 1

In triangles AOC and BOD, we have

AO = BO (O, the midpoint of AB);

∠AOC=∠BOD, (vertically opposite angles);

CO=OD, (O, the midpoint of CD)

So by SAS postulate we have

△AOC≅△BOD.

Hence, AC = BD, as they are corresponding parts of congruent triangles.