# 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 CD Par AE and CY Par BA

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 ABCDE is Any Pentagon

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 X and Y Are the Mid-Points of AC and AB

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