# NCERT Mathematics Class 9 Exemplar Ch 9 Areas of Parallelograms and Triangles Part 6

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Q.5. ABCD is a square. E and F are respectively the midpoints of BC and CD. If R is the mid-point of EF (Fig), prove that

Q.6. O is any point on the diagonal PR of a parallelogram PQRS (Fig). Prove that

Q.7. ABCD is a parallelogram in which BC is produced to be such that (Fig). AE intersects CD at F. If ar , find the area of the parallelogram ABCD.

Answer:

Q.8. In trapezium ABCD, and L is the mid-point of BC. Through L, a line has been drawn which meets AB in P and DC produced in Q (Fig). Prove that

Q.9. If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram so formed will be half of the area of the given quadrilateral (Fig).