Question

In the given figure, $AC=BD$. Prove that $AB=CD$.

Answer 1

From the given figure, we have:

$\Rightarrow AC=AB+BC$

$\Rightarrow BD=BC+CD$

It is given that $AC=BD$.

So, $AB+BC=BC+CD$..................(1)

According to Euclid's axiom, when equals are subtracted from equals, the remainders are also equal.

Subtracting $BC$ from both sides in equation (1), we get:

$\Rightarrow AB+BC-BC=BC+CD-BC$

$\Rightarrow AB=CD$

Hence proved.