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 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 : In $\triangle$ABC and $\triangle$PQR, AB = PQ and $\angle$B = $\angle$Q. The two triangles are congruent by SAS criteria if:

Option 1: BC = QR

Option 2: AC = PR

Option 3: AC = QR

Option 4: BC = PQ

Question : In $\triangle$ABC, D and E are points on the sides BC and AB, respectively, such that $\angle$ACB = $\angle$ DEB. If AB = 12 cm, BE = 5 cm and BD : CD = 1 : 2, then BC is equal to:

Option 1: $8 \sqrt{3}$ cm

Option 2: $5 \sqrt{5}$ cm

Option 3: $6 \sqrt{5}$ cm

Option 4: $6 \sqrt{3}$ cm