# NCERT Mathematics Class 9 Exemplar Ch 9 Areas of Parallelograms and Triangles Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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