Question

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Then, AC = BD.

• A. True
• B. False

Answer 1

The correct option is A

True

ABCD is an isosceles trapezium (given)
Hence, $\angle ADC=\angle BCD$ ... (base angles of an isosceles trapezium)
In $△ADC$ and $△BCD$,
$\left(i\right)AD=BC$
$\left(ii\right)\angle ADC=\angle BCD$ ...(base angles of an isosceles trapezium)
$\left(iii\right)DC=Dc$ ...(common)
$\left(iv\right)△ADC\cong △BCD$ ...(SAS Postulate)
$\left(v\right)AC=BD$ ...(cpct)