# NCERT Mathematics Class 9 Exemplar Ch 8 Quadrilaterals Part 5

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**Exercise 8.3**

Q.1. One angle of a quadrilateral is of and the remaining three angles are equal. Find each of the three equal angles.

Answer:

Q.2. ABCD is a trapezium in which and. Find angles C and D of the trapezium.

Answer: each

Q.3. The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is. Find the angles of the parallelogram.

Answer:

Q.4. ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Answer:

Q.5. E and F are points on diagonal AC of a parallelogram ABCD such that. Show that BFDE is a parallelogram.

Q.6. E is the mid-point of the side AD of the trapezium ABCD with. A line through E drawn parallel to AB intersects BC at F. Show that F is the mid-point of BC.

Q.7. Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC as shown in Fig. Show that QR.

Q.8. D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral triangle ABC. Show that ∆ DEF is also an equilateral triangle.

Q.9. Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that (Fig. 8.6). Show that AC and PQ bisect each other.

Q.10. In Fig, P is the mid-point of side BC of a parallelogram ABCD such that. Prove that.