#### Chapter 14 Quadrilaterals R.D. Sharma Solutions for Class 9th Exercise 14.3

**Exercise 14.3**

1. In a parallelogram ABCD, determine the sum of angles ∠C and ∠D.

**Solution**

2. In a parallelogram ABCD, if ∠B = 135°, determine the measure of its other angles.

**Solution**

3. ABCD is a square. AC and BD intersect at O. State the measure of ∠AOB.

**Solution**

4. ABCD is a rectangle with ∠ABD = 40°. Determine ∠DBC.

**Solution**

5. The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.

**Solution**

6. P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove that CQ is parallel to AP. Prove also that AC bisects PQ.

**Solution**

7. ABCD is a square E, F, G and H are points on AB, BC, CD and DA respectively. such that AE = BF = CG = DH. Prove that EFGH is a square.

**Solution**

8. ABCD is a rhombus, EABF is a straight line such that EA = AB = BF. Prove that ED and FC when produced meet at right angles.

**Solution**

9. ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC

**Solution**