Question

In the figure, if $AC=BD$, then prove that $AB=CD$.

Answer 1

Given,

$AC=BD$ ... (i)

$AC=AB+BC$ ……(ii) (Point $B$ lies between $A$ and $C$)

$BD=BC+CD$ … (iii) (Point $C$ lies between $B$ and $D$)

Now,

substituting (ii) and (iii) in (i), we get

$\Rightarrow AB+BC=BC+CD$

$\Rightarrow AB+BC–BC=CD$

$\Rightarrow AB=CD$

Hence, $AB=CD$.