Question

Suppose line segments AB and CD intersect at O in
such a way that AO = OD and OB = OC. Prove that:
AC = BD but AC may not be parallel to BD.

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Answer 1

Step-by-step explanation:

Join AC and BD.

Given, AO= DO

CO= BO

To prove- AC= BD

Proof: In triangle AOC and DOB, we have:

AO= DO ( Given)

Angle AOC= Angle DOB (vertically opposite angles are equal)

CO= BO (Given)

So triangle AOC is congruent to Traingle DOB.

By CPCT, AC= BD.

Hence Proved.