Question

AB & CD bisect each other at Least.Prove that AC=BD.

Answer 1

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We would be using the concept of Congruency to solve this question.

Firstly, let's note down the information provided to us:-

AB and CD bisect each other.

Now, Join AC and BD so that they form two triangles.

In Triangles ACK and KBD:-

AK = KB ( AB and CD bisect each other)

CK = KD ( AB and CD bisect each other)

∠CKA = ∠DKB (Vertically Opposite Angles)

Here, we have 2 sides and and one angle between them equal in both the triangles.

Hence, ΔACK ≅ ΔDKB    ...(SAS)

Therefore, AC = BD     ...(CPCT)

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