InterviewSolution
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InterviewSolution
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In the adjoining figure, ABCD is a parallelogram, P and Q are midpoints of sides AB and DC respectively, then prove APCQ is a parallelogram. |
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Answer» Given: ABCD is a parallelogram. P and Q are the midpoints of sides AB and DC respectively. To prove: APCQ is a parallelogram. Proof: AP = (1/2) AB …..(i) [P is the midpoint of side AB] QC = (1/2) DC ….(ii) [Q is the midpoint of side CD] ABCD is a parallelogram. [Given] ∴ AB = DC [Opposite sides of a parallelogram] ∴ (1/2) AB = (1/2) DC [Multiplying both sides by 1/2] ∴ AP = QC ….(iii) [From (i) and (ii)] Also, AB || DC [Opposite angles of a parallelogram] i.e. AP || QC ….(iv) [A – P – B, D – Q – C] From (iii) and (iv), APCQ is a parallelogram. [A quadrilateral is a parallelogram if its opposite sides is parallel and congruent] |
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