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 : $\triangle PQR$ is an isosceles triangle and $PQ=PR=2a$ unit, $QR=a$ unit. Draw $PX \perp QR$, and find the length of $PX$.

Option 1: $\sqrt{5} a$

Option 2: $\frac{\sqrt{5} a}{2}$

Option 3: $\frac{\sqrt{10} a}{2}$

Option 4: $\frac{\sqrt{15} a}{2}$

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 : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:

Option 1: 10 cm

Option 2: 13 cm

Option 3: 8 cm

Option 4: 11 cm

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 = $60^{\circ}$