Question : If $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}, \mathrm{BC}=6 \mathrm{~cm}$, and $\angle \mathrm{A}=75^{\circ}$, then which one of the following is true?
Option 1: $\mathrm{QR}=6$ cm, $\angle \mathrm{R}=75^{\circ}$
Option 2: $\mathrm{QR}=6$ cm, $\angle \mathrm{Q}=75^{\circ}$
Option 3: $\mathrm{QR}=6$ cm, $\angle \mathrm{P}=75^{\circ}$
Option 4: $\mathrm{PR}=6$ cm, $\angle \mathrm{P}=75^{\circ}$
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Correct Answer: $\mathrm{QR}=6$ cm, $\angle \mathrm{P}=75^{\circ}$
Solution :
Given, $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}$
And, $\mathrm{BC}=6 \mathrm{~cm}$, and $\angle \mathrm{A}=75^{\circ}$
Since $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}$,
$BC = QR = 6$ cm (corresponding sides of congruent triangles)
And, $\angle \mathrm{A}=\angle \mathrm{P}=75^{\circ}$ (corresponding angles of congruent triangles)
Hence, the correct answer is $QR=6$ cm, $\angle \mathrm{P}=75^{\circ}$.
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