Construction of Quadrilaterals - II

A quadrilateral is a polygon with four sides.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

Rectangle is a quadrilateral having four right angles.

Rhombus is a quadrilateral with all sides equal in length.

Square is a quadrilateral with all sides equal in length and all angles of equal measure each 90°.

A parallelogram can be constructed uniquely if

    two consecutive sides and included angle are given.

    one side and both the diagonals are given.

    two consecutive sides and one diagonal are given.

    two diagonals and included angle are given.

    two adjacent sides and height are given.

    When two adjacent sides and three angles are given.

A trapezium can be constructed when four sides are given.

Some special cases:

    Construction of a square when one of the sides is given.

    Construction of a rhombus when the lengths of two diagonals are given.

    Construction of a rectangle when two adjacent sides are given.

Mathematical constructions have many applications in our real life. The most common application is in designing in the construction industry.

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  • Q1

    Can we construct a parallelogram if its two diagonals are 12 cm and 4 cm respectively? If yes, how many are possible?

    Marks:1
    Answer:

    Yes, we can construct a parallelogram if its diagonals
    are given, using the fact that diagonals of a parallelogram bisect each other but there are infinitely many such parallelograms.

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  • Q2

    How many parallelograms can we construct if their adjacent sides are 8 cm and 4 cm respectively?

    Marks:1
    Answer:

    There are infinitely many parallelograms with the two given adjacent sides.

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  • Q3

    Construct a regular hexagon of side 4 cm inside a circle of radius 4 cm. Write the steps of construction also.

    Marks:3
    Answer:


    Steps of construction:
    · Draw a circle of radius 4 cm.
    · Take a point 'A' on the circumference. With A as centre and radius 4 cm, draw two arcs that cut the circle at B and F.
    · With B as centre and radius 4 cm, draw an arc that cuts the circle at C.
    · With C as centre and radius 4 cm, draw an arc that cuts the circle at D.
    · With D as centre and radius 4 cm, draw an arc that cuts the circle at E.
    · Join AB, BC, CD, DE, EF and FA.
    ABCDEF is the required hexagon.

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  • Q4

    Write the steps of construction to complete the following figure as a hexagon ABCDEF.

    Marks:2
    Answer:


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  • Q5

    Write the steps of construction to complete the following figure as a parallelogram ABCD.

    Marks:2
    Answer:

    Step1: Draw an arc of radius 6 cm with B as centre.

    Step2: Draw an arc of radius 8 cm with D as centre that
    cuts the previous arc at C.

    Step 3: Join BC and DC.

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