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: $ar(\triangle ABC)=ar(\triangle PQR)$
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Correct Answer: $ar(\triangle ABC)\neq ar(\triangle PQR)$
Solution : Given: In a $\triangle ABC$, if $\angle A=90^{\circ}, AC=5 \mathrm{~cm}, BC=9 \mathrm{~cm}$ and in $\triangle PQR, \angle P=90^{\circ}, PR=3 \mathrm{~cm}, QR=8$ $\mathrm{cm}$ Since the sides are not equal, $\triangle ABC \cong \triangle PQR$ is wrong. In $\triangle ABC$, $AB=\sqrt{9^2-5^2}=\sqrt{56} =2\sqrt{14}$ Area of $\triangle ABC = \frac{1}{2}\times 5 \times 2\sqrt{14} =5\sqrt{14} =\sqrt{350}$ cm$^2$ In $\triangle PQR$, $PQ=\sqrt{8^2-3^3}=\sqrt{55}$ cm Area of $\triangle PQR = \frac{1}{2}\times 3 \times \sqrt{55} = \sqrt{247.5}$ cm$^2$ Hence, the correct answer is $ar(\triangle ABC)\neq ar(\triangle PQR)$.
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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?
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 $\angle PRQ$?
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?
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?
Question : Let ABC and PQR be two congruent triangles such that $\angle $A = $\angle $P = $90^{\circ}$. If BC = 13 cm, PR = 5 cm, find AB.
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