If tringle PQR congruent to triangle ABC, BC = 6 cm ang B = 50° and ang A = 70° , then which of the following is true ?
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Correct answer: D
Explanation
The correct answer is option 4 i.e. QR = 6 cm , ∠R = 60°.
Given that, triangle PQR is congruent to triangle ABC
BC = 6 cm
Angle B = 50° and angle A = 70°
Sum of all the angles of a triangle is 180°.
When two triangles are congruent, the measure of their corresponding sides and angles are equal.
According to the given question,
Triangle PQR is congruent with traingle ABC,
⇒ AB = PQ, BC = QR and AC = PR
And angle A = angle P, angle B = angle Q and angle C = angle R
Now, angle A + angle B + angle C = 180°
⇒ 70° + 50° + angle C = 180°
⇒ Angle C = 180° - 120°
⇒ Angle C = 60°
So, angle P = 70° , angle Q = 50° and angle R = 60°
Also, BC = QR = 6 cm
Hence the required answer is QR = 6 cm , ang R = 60°.