Question

State the congruency of following pairs of triangles.

In $\Delta ABC$ and $\Delta PQR$, $BC=QR,$ $\angle A={90}^{\circ },\angle C=\angle R={40}^{\circ }$ and $\angle Q={50}^{\circ }$.

• A. $ASA$
• B. $SSS$
• C. $SAS$
• D. Not congruent

Answer 1

The correct option is A $ASA$

In $△ABC$,
$\angle A={90}^o$, $\angle C={40}^o$
Sum of all angles of a triangle $={180}^o$
$\angle A+\angle B+\angle C={180}^o$
${90}^o+\angle B+{40}^o={180}^o$
$\therefore \angle B={50}^{\circ }$
Now, In $△ABC$ and $△PQR$
$BC=QR$ (Given)
$\angle C=\angle R={40}^o$ (Given)
$\angle B=\angle Q={50}^o$
Thus, $△ABC\cong △PQR$ (ASA rule)