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, $\angle \mathrm{P}=75^{\circ}$
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Correct Answer: $\mathrm{QR}=6$ cm, $\angle \mathrm{P}=75^{\circ}$
Solution : Given, $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}$ And, $\mathrm{BC}=6 \mathrm{~cm}$, and $\angle \mathrm{A}=75^{\circ}$ Since $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}$, $BC = QR = 6$ cm (corresponding sides of congruent triangles) And, $\angle \mathrm{A}=\angle \mathrm{P}=75^{\circ}$ (corresponding angles of congruent triangles) Hence, the correct answer is $QR=6$ cm, $\angle \mathrm{P}=75^{\circ}$.
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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:
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 : 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 : $\triangle ABC$ 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 : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.
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