Question

How to prove a diagonal bisects two angles

Answer 1

ABCD is a parallelogram, diagonals AC and BD intersect at O

In triangles AOD and COB,

DAO = BCO (alternate interior angles)

AD = CB

ADO = CBO (alternate interior angles)

AOD COB (ASA)

Hence, AO = CO and OD = OB (c.p.c.t)

Thus, the diagonals of a parallelogram bisect each other.

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