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 : It is given that ABC $\cong$ PQR, AB = 5 cm, $\angle$B = $40^{\circ}$, and $\angle$A = $80^{\circ}$. Which of the following options is true?

Option 1: PQ = 5 cm and $\angle$R = $60^{\circ}$

Option 2: QR = 5 cm and $\angle$R = $60^{\circ}$

Option 3: QR = 5 cm and $\angle$Q = $60^{\circ}$

Option 4: PQ = 5 cm and $\angle$P = $60^{\circ}$

Question : If it is given that for two right-angled triangles $\triangle$ABC and $\triangle$DFE, $\angle$A = 25°, $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED, then which one of the following is TRUE?

Option 1: $\triangle \mathrm{ABC} \cong \triangle \mathrm{FED}$

Option 2: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DFE}$

Option 3: $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$

Option 4: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DEF}$

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 : 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