# NCERT Mathematics Class 9 Exemplar Ch 9 Areas of Parallelograms and Triangles Part 7

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**Exercise 9.4**

Q.1. A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that

Q.2. The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Q.3. The medians BE and CF of a triangle ABC intersect at G. Prove that the area of area of the quadrilateral AFGE.

Q.4. In Fig, and Prove that

Q.5. ABCD is a trapezium in which, and. If X and Y are, respectively the mid-points of AD and BC, prove that

Q.6. In ∆ ABC, if L and M are the points on AB and AC, respectively such that. Prove that

Q.7. In Fig. 9.25, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that

Q.8. If the medians of a ∆ ABC intersect at G, show that

Q.9. In Fig, X and Y are the mid-points of AC and AB respectively, and CYQ and BXP are straight lines. Prove that

Q.10. In Fig, ABCD and AEFD are two parallelograms. Prove that