Question

If $\mathrm{AB}=\mathrm{QR},\mathrm{BC}=\mathrm{PR}$and $\mathrm{CA}=\mathrm{PQ}$, then

• A. $\Delta ABC\cong \Delta PQR$
• B. $\Delta CBA\cong \Delta PRQ$
• C. $\Delta BAC\cong \Delta RPQ$
• D. $\Delta PQR\cong \Delta BCA$

Answer 1

The correct option is B

$\Delta CBA\cong \Delta PRQ$

Step 1: Explanation of the correct option:

Option $\mathrm{B}$: It is the correct option

Given,

$$\begin{gathered} AB=QR \\ BC=PR \\ CA=PQ \end{gathered}$$

From here, we can see that,

$\mathrm{A}$ equivalent to $\mathrm{Q}$

$B$equivalent to$\mathrm{R}$

$C$equivalent to $P$.

$\therefore \Delta CBA\cong \Delta PRQ$ , [$\mathrm{SSS}$criteria]

Step 2: Explanation of the incorrect option

option $\mathrm{A}$ : not correct because $\mathrm{A},\mathrm{B}$ and $C$ are not corresponding to $P,Q$ and $R$ respectively.

option$C$ : not correct because $B,A$and $C$ are not corresponding to $R,P$and $Q$ respectively.

option$D$ : not correct because $B,C$ and $A$ are not corresponding to$P,Q$ and $R$ respectively.

Hence, the correct option is $\mathrm{B}$.