r are the midpoints of sides ab – Discussion Forum

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Virat

Asked: September 30, 2026In: Class 9 Maths

(i) If P, Q, R are the midpoints of sides AB, AC, BC respectively of △ABC, show that △PQR is congruent to △QPA and to two other triangles which you should identify. (ii) Suppose someone erases △ABC, leaving only △PQR on the paper. Can you reconstruct △ABC from △PQR?

(i) By the Midpoint Theorem, PQ = BC/2 = BR = RC, QR = AB/2 = AP = PB and PR = AC/2 = AQ = QC, so △PQR ≅ △QPA ≅ △RPB ≅ △CQR by SSS. (ii) Yes, construct ...