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, $\angle \mathrm{P}=75^{\circ}$

Question : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.

Option 1: 6 cm

Option 2: 3 cm

Option 3: 5 cm

Option 4: 8 cm

Question : In a $\triangle ABC$, if $\angle A=90^{\circ}, AC=5 \mathrm{~cm}, BC=9 \mathrm{~cm}$ and in $\triangle PQR, \angle P=90^{\circ}, PR=3 \mathrm{~cm}, QR=8$ $\mathrm{cm}$, then:

Option 1: $\triangle ABC \cong \triangle PQR$

Option 2: $ar(\triangle ABC)\neq ar(\triangle PQR)$

Option 3: $ar(\triangle ABC) \leq ar(\triangle PQR)$

Option 4: $ar(\triangle ABC)=ar(\triangle PQR)$

Question : $\triangle ABC$ and $\triangle PQR$ are two triangles. AB = PQ = 6 cm, BC = QR =10 cm, and AC = PR = 8 cm. If $\angle ABC = x$, then what is the value of $\angle PRQ$?

Option 1: $(180 ^{\circ}–x)$

Option 2: $x$

Option 3: $(90 ^{\circ}–x)$

Option 4: $(90 ^{\circ}+x)$

Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.

Option 1: $5 \sqrt{3}~cm$

Option 2: $3 \sqrt{3}~cm$

Option 3: $\frac{1}{\sqrt{3}}~cm$

Option 4: $\frac{5}{\sqrt{3}}~cm$