Properties of Quadrilateral

A quadrilateral is a closed shape bounded by four line segments.

The line segments joining any two non-consecutive 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:1
    Answer:

    Equal and parallel

    Explanation:

    A quadrilateral is a parallelogram, if a pair of opposite sides is equal and parallel.

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  • Q2

    In the given figure, ABCD is a parallelogram. The value of x is:

    Marks:1
    Answer:

    105°

    Explanation:

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  • Q3

    In a parallelogram ABCD, D = 100°. The measures of A and B are

    Marks:1
    Answer:

    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°

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  • Q4

    In the figure, ABCD is a parallelogram. The values of x and y are

    Marks:1
    Answer:

    4 and 9 respectively

    Explanation:

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  • Q5

    PQRS is a parallelogram. The values of SQP and QSP are

    Marks:1
    Answer:

    45° and 60° respectively

    Explanation:

    QSP = RQS [Alternate angles]

    QSP = 60°

    QSP + P + SQP = 180°

    60° + 75° + SQP = 180°

    SQP = 180° - 135° = 45°

    View Answer