In the adjoining figure, ABCD is a parallelogram. If P and Q are mid-points of sides CD and BC respectively. Show that CR = AC.

Question

KnowledgeBoat · Accepted Answer

In parallelogram, diagonals bisect each other. ∴ AO = OC = AC ......(i) In △BCD, P and Q are midpoints of CD and BC, PQ || BD (By midpoint theorem) Since, PQ || BD ∴ QR || BO In △BCO, Q is midpoint of BC and QR || BO ∴ R is midpoint of OC CR = OC Substituting value of OC from (i) in above equation, CR = OC = AC = AC. Hence, proved that CR = AC.

Mathematics

In the adjoining figure, ABCD is a parallelogram. If P and Q are mid-points of sides CD and BC respectively. Show that CR = AC.

Mid-point Theorem

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