$A B$ and $C D$ bisect each other at $O$ . Prove that $A C = B D$

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Solution

Given: $O$ is mid point of $A B$ and $C D$
$∴$ $A O = O B$ and $C O = O D$
To prove: $A C = B D$
Proof: Consider $△ A O C$ and $△ B O D$
$A O = O B$ (given)
$C O = O D$ (Given)
$∠ A O C = ∠ B O D$ (Vertically Opposite angle)
$△ A O C \equiv △ B O D$
Hece we get, $A C = B D$ (by c.p.c.t.c)

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