Question

ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, then the total number of parallelograms are:
(a) 2
(b) 5
(c) 6
(d) 4

Answer 1

The ABCD is frist parallelogram and PQRS is second parallelogram so 2 is right answer

Answer 2

ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, then the total number of parallelograms are 6

Therefore, Option (c) is correct.

Step-by-step explanation:

The figure is attached.

It can be easily proved that

1. APDQ is a parallelogram

2. PQBC is a parallelogram

3. APCQ is a parallelogram

4. BPDQ is a parallelogram

5. PSQR is a parallelogram

6. Also it is given that ABCD is a parallelogram

Therefore, total number of parallelograms are 6

Hope this answer is helpful.

Know More:

Q: ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see the below figure). If AQ intersects DP at S and BQ intersects CP at R, show that:

(i) APCQ is a parallelogram.

(ii) DPBQ is a parallelogram.

(iii) PSQR is a parallelogram.

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