Question

$\Delta ACQ$ and $\Delta ASB$ are congruent.

State whether the above statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given: ABPQ and ACRS are squares.
$\angle CAQ=\angle BAQ+\angle BAC$
$\angle CAQ=\angle BAC+90$ (I)
$\angle BAS=\angle BAC+\angle CAS$
$\angle BAS=\angle BAC+90$ (II)
From I and II,
$\angle CAQ=\angle BAS$ ...(III)
In $△ACQ$ and $△ASB$,
$\angle CAQ=\angle BAS$ (From III)
$AQ=AB$ (ABPQ is a square)
$AC=AS$ (ACRS is a square)
Thus, $△ACQ\cong △ASB$ (SAS congruency)