Question

$\Delta ABC\cong \Delta PQR$. If AB $=$ 5 cm, $\angle B={40}^{\circ }$ and $\angle A={80}^{\circ },$ then which of the following is true.

• A. $QP=5$ cm, $\angle P={60}^{\circ }$
• B. $QP=5$ cm, $\angle R={60}^{\circ }$
• C. $QR=5$ cm, $\angle R={60}^{\circ }$
• D. $QR=5$ cm, $\angle Q={40}^{\circ }$

Answer 1

Answer: (B)

$QP=5$ cm, $\angle R={60}^{\circ }$

Applying angle sum property of triangle in $△ABC$

$\angle A+\angle B+\angle C={180}^{\circ }{80}^{\circ }+{40}^{\circ }+\angle C=1{80}^{\circ }\Rightarrow \angle C={60}^{\circ }$

Given $△ABC\cong PQR$

Now corresponding parts of congruent triangle are equal

$\therefore QP=BA=AB$

$\Rightarrow QP=5cm$

and $\angle R=\angle C$

$\Rightarrow \angle R={60}^{\circ }$