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Question

In the figure below, two vertices of a parallelogram are joined to the mid points of two sides. Then, the lines divide the diagonal in the picture into _______ equal parts.

  1. 3

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Solution

The correct option is A 3

In parallelogram ABCD, M is the midpoint of AB, N is the midpoint of DC.

AM = MB, DN = NC

In parallelogram ABCD, AB = CD

AB2=CD2=AM=DN

AM = BM = DN = NC .....(i)

DM and BN are parallel lines.

Draw 2 lines through A & C parallel to DM.

From (1), these parallel lines are equidistant.

Thus, parallel lines DM & BN divide AC into 3 equal parts.

AP = PQ = QC


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