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

a. Proof questions

b. Difficult problems

c. Long answer questions

a. Proof questions

b. Difficult problems

c. Long answer questions

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

Solution

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

Solution

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

Solution

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

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

(i) AE = BE

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

Solution

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

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

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

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

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

Solution

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

Solution

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

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

Solution

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

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

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

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

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

In a parallelogram ABCD, $\angle D = 135^0$, determine the angles measures of $\angle A \; and \; \angle B$

Solution

ABCD is a parallelogram in which $\angle A = 70^0$. Compute $\angle B \; ,\; \angle C \;and \; \angle D$

Solution

ABCD is a parallelogram in which $\angle DAB = 75^0$ and $\angle DBC = 60^0$. Compute $\angle CDB \; and \; \angle ADB$.

Solution

ABCD is a parallelogram and X, Y are the mid- points of sides AB and DC respectively. Show that in parallelogram ABCD, AXCY is a parallelogram.

Solution

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

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

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.

This Quadrilaterals Worksheet for Class 9 Maths with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.

**Notes****Assignments & NCERT Solutions**

Class 9 Maths Class 9 Science