Given below are the **Class 9 Maths** Worksheet for Quadrilaterals

a. Concepts questions

b. Calculation problems

c. Multiple choice questions

d. Long answer questions

e. Fill in the blanks

**Question 1**
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that :

(i) $ \Delta APB \cong \Delta CQD$

(ii) AP = CQ

**Question 2**
The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the angles of the quadrilateral.

**Question 3** In a quadrilateral ABCD, AO and BO are the bisectors of $\angle A \; and \; \angle B$ respectively. Prove that $\angle AOB = \frac {1}{ 2} (\angle C + \angle D)$

**Question 4** In the figure, ABCD is a parallelogram. E is the mid-point of BC. DE and AB when produced meet at F. Prove that AF = 2AB

**Question 5** ABCD is a square and on the side DC, an equilateral triangle is constructed. Prove that

(i) AE = BE

(ii) $\angle DAE = 15^0$

**Question 6** ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

**Question 7** If ABCD is a trapezium in which AB || CD and AD = BC, prove that ∠A = ∠B

**Question 8** In the figure, diagonal BD of parallelogram ABCD bisects ∠B. Show that it bisects ∠D also

**Question 9** E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

**Question 10** The two opposite angles of a parallelogram are $(3y - 10)^0$ and $(2y + 35)^0$. Find the measure of all the four angles of the parallelogram

**Question 11** ABCD is a rhombus in which AC = 16 cm and BC = 10 cm. Find the length of the diagonal BD.

**Question 12** Diagonals of a quadrilateral ABCD bisect each other. If ∠A = 35°, then ∠B = 145°. Is it true ? Justify your answer.

**Question 13** Can $\angle 95^0 \; ,\; 70^0 \; ,\; 110^0 \; and \; 80^0$ be the angles of a quadrilateral ? Why or why not ?

**Question 14** Prove that quadrilateral formed by bisectors of the angles of a parallelogram is a rectangle.

**Question 15** Show that the line segments joining the mid-points of opposite sides of quadrilateral bisect each other.

**Question 16** ABCD is a parallelogram in which X and Y are the mid-points of AB and CD. AY and DX are joined which intersect each other at P. BY and CX are also joined which intersect each other at Q. Show that PXQY is a parallelogram

**Question 17**Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus

**Question 18**If one angle of a parallelogram is a right angle, it is a rectangle. Prove.

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