Properties of Quadrilateral
A quadrilateral is a closed shape bounded by four line segments.
The line segments joining any two nonconsecutive vertices of a quadrilateral are called its diagonals.
Types of quadrilateral are:
Parallelogram: A parallelogram is a quadrilateral that has two pairs of parallel sides.
Trapezium: A quadrilateral with one pair of parallel sides is called trapezium.
Square: Square is a quadrilateral with all sides equal in length and all angles of equal measure each 90°.
Rhombus: Rhombus is a quadrilateral with all sides equal in length.
Kite: A kite is a quadrilateral with two distinct pairs of adjacent sides which are equal in length.
Rectangle: Rectangle is a quadrilateral having four right angles.
A square is a rectangle and also a rhombus.
A rectangle or a rhombus is not a square.
A trapezium is not a parallelogram.
A kite is not a parallelogram.
A parallelogram is a trapezium.
Angle Sum Property: The sum of all the angles of a quadrilateral is 360°.
Results on Parallelogram:
A diagonal of a parallelogram divides it into two congruent triangles.
In a parallelogram,
opposite sides are equal.
opposite angles are equal.
diagonals bisect each other.
A quadrilateral is a parallelogram, if
opposite sides are equal.
opposite angles are equal.
diagonals bisect each other.
a pair of opposite sides is equal and parallel.
A quadrilateral is a parallelogram, if a pair of opposite sides is equal and parallel.
The diagonals of a rectangle are equal and conversely if the diagonals of a parallelogram are equal, it is a rectangle.
The diagonals of a rhombus bisect each other at right angles and conversely if the diagonals of a parallelogram cut at right angles, it is a rhombus.
The diagonals of a square are equal and perpendicular to each other and conversely if the diagonals of a parallelogram are equal and perpendicular to each other, then parallelogram is a square.
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Q1
A quadrilateral is a parallelogram if a pair of opposite sides is
Marks:1Answer:
Equal and parallel
Explanation:
A quadrilateral is a parallelogram, if a pair of opposite sides is equal and parallel.

Q2
In the given figure, ABCD is a parallelogram. The value of x is:
Marks:1Answer:
105°
Explanation:

Q3
In a parallelogram ABCD, D = 100°. The measures of A and B are
Marks:1Answer:
80°, 100° respectively.
Explanation:
In a parallelogram ABCD, D = 100°
And A + D = 180°
Then, A = 180°  100° = 80°
And 80° + B = 180°
B = 180°  80° = 100° 
Q4
In the figure, ABCD is a parallelogram. The values of x and y are
Marks:1Answer:
4 and 9 respectively
Explanation:

Q5
PQRS is a parallelogram. The values of SQP and QSP are
Marks:1Answer:
45° and 60° respectively
Explanation:
QSP = RQS [Alternate angles]
QSP = 60°
QSP + P + SQP = 180°
60° + 75° + SQP = 180°
SQP = 180°  135° = 45°