Question

In Fig., if $AC=BD$, then $AB=CD$.

• A. True
• B. False

Answer 1

The correct option is A True

Given that $AC=BD$ ....(1)
$AC=AB+BC$
[point B lies between A and C] ....(2)
$BD=BC+CD$
[point C lies between B and D] .....(3)
Substituting (2) and (3) in (10, we get:
$AB+BC=BC+CD$
$AB+BC-BC=CD$
So, $AB=CD$
[ if equals are subtracted from equals, the remaining are equal]