Question

Which of the following statement(s) is/are correct for the above two triangles?

• A. $\text{CA = QR}$
• B. $\angle CAB=\angle QRP$
• C. $△BCA\cong △PQR$
• D. $\angle CAB=\angle QPR$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\text{CA = QR}$
B $\angle CAB=\angle QRP$
C $△BCA\cong △PQR$

In $△$PQR,
$\angle P=180°-(\angle Q+\angle R).$
$\Rightarrow \angle P=180°-(60°+50°)$
$\Rightarrow \angle P=70°$

Now, in triangles, $△BCA\text{and}△PQR$
$BC=PQ=5cm$
$\angle B=\angle P=70°$
$AB=RP=7cm.$

So, by SAS criterion for congruency of triangles,
$△BCA\cong △PQR.$