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D and E are mid-points of the sides AB and AC of △ABC and O is any point on the side BC. O is joined to A. If P and Q are mid-points of OB and OC respectively, then DEQP is

  1. a square

  2. a rectangle

  3. a rhombus

  4. a parallelogram

Mid-point Theorem

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Answer

In △ABC,

D and E are mid-points of AB and AC of △ABC and O is any point on the side BC. O is joined to A. If P and Q are mid-points of OB and OC, then DEQP is? Mid-point Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

D and E are respective midpoints of AB and AC.

∴ DE || (BC or PQ) ……(1)

Again in △ABO,

D and P are respective midpoints of AB and BO.

∴ DP || AO ……..(2)

In △ACO,

E and Q are respective midpoints of AC and CO.

∴ EQ || AO ……..(3)

From 2 and 3 we get,

DP || EQ …….(4)

From 1 and 4 we get,

DE || PQ and DP || EQ

∴ DEQP is a parallelogram.

Hence, Option 4 is the correct option.

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