EASY
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In the given figure, ABCD is a parallelogram whose diagonals intersect each other at O. Through O,PQ is drawn then prove that OP=OQ.

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Important Questions on Quadrilaterals

EASY
In a quadrilateral ABCD, the bisector of C and D meet at E. If CED=56° and A=49°, then the measure of B is: 
MEDIUM
If angles of a quadrilateral are in the ratio 3:5:9:13, find the largest angle.
EASY
In quadrilateral PQRS, RMQS, PNQS and QS=6cm. If RM=3cm and PN=2cm, then the area of PQRS is:
MEDIUM
In quadrilateral ABCD, the bisectors of A and B meet at O and AOB=64°, C+D=?
EASY
If the measure of each interior angle of a regular polygon is 135°, then the number of its sides is
MEDIUM
PQRS is a cyclic quadrilateral in which PQ=14.4 cm, QR=12.8 cm and SR=9.6 cm. If PR bisects QS, what is the length of PS?
EASY
In the given figure, if AB=10 cmCD=7 cmSD=4 cm and AS=5 cm, then BC=?
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MEDIUM

A circle is inscribed in quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q,R and S, respectively. If As=6cm, BC=12cm and CR=5cm, then the length of AB (in cm) is

MEDIUM

How many quadrilaterals are there in the given figure?

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HARD
Let ABC be a triangle with sides a,b,c. Then lengths of medians of the triangle formed by the medians of the triangle ABC are
MEDIUM
From a point P, which is at a distance of 13 cm from the centre O of a circle, a pair of tangents PQ and PR of length 12 cm are drawn to the circle. The area of the quadrilateral PQOR (in cm2) is:
EASY
Shape made by the bisectors of angles of a parallelogram is
MEDIUM
Vertices A, B,C and D of a quadrilateral ABCD lie on a circle, A is three times C andD is two timesB . What is the difference between the measures of D and C?
EASY
In a circle with centre OAC and BD are two chords. AC and BD meet at E when produced. If AB is the diameter and AEB=68°, then the measure of DOC is:
EASY
Three acute angles of a quadrilateral are 82° each. Find out the fourth angle. 
MEDIUM
In quadrilateral ABCDB=90°,C-D=60° and A-C-D=10°. Find the measure of the smallest angle of this quadrilateral.
MEDIUM

Let ABCD be a square. An arc of a circle with A as centre and AB as radius is drawn inside the square joining the points B and D. Points P on AB, S on AD, Q and R on arc BD are taken such that PQRS is a square. Further suppose that PQ and RS are parallel to AC. Then,  area PQRS area ABCD is

 

MEDIUM

In figure,  ABCD is a parallelogram. Point E is on the ray AB such that BE=AB, then prove that line ED bisects segment BC at point F.

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EASY
The diagonals of a rectangle bisects each other at 90°.
MEDIUM

Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.