Quadrilaterals are broadly classified into two categories: parallelograms(quadrilaterals with
two pair of parallel sides) and trapeziums(quadrilaterals having only one pair of parallel
sides) Write down the names of four-sided figures which come under each of these
categories. Also draw the shape and write down all the properties of each.
Is there any other quadrilateral which does not fall in these categories. Draw and write its
properties.
Answers
Properties
A quadrilateral has:
four sides (edges)
four vertices (corners)
interior angles that add to 360 degrees:
Types of Quadrilaterals
Parallelogram
Square :
All sides are congruent
Each interior angle measures 90∘<
Diagonals are equal and are perpendicular bisectors of each other
Every square is a parallelogram in which diagonals are congruent and bisect the angles
Every square is a rectangle and a rhombus
Rectangle :
All angles in a rectangle are right angles
Opposite sides are equal in a rectangle
Diagonals are congruent and bisect each other
Every rectangle is a parallelogram with at least one right angle
Rhombus :
All sides are congruent
Diagonals are perpendicular bisectors of each other
Each diagonal isthe angle bisector of both the opposite angles
Every rhombus is a parallelogram and a kitewith all sides of equal length
Trapezium
In trapezium, exactly one pair of opposite sides are parallel
The diagonals intersect each other
The non-parallel sides in the trapezium are unequal except in isosceles trapezium
The line that joins the mid-points of the non-parallel sides is always parallel to the bases or parallel sides which is equal to half the sum of the parallel sides.
Isosceles trapezium – The legs or the non-parallel sides of the trapezium are of equal length
Scalene Trapezium – A trapezium with all the sides and angles of different measures
Right Trapezium – A right trapezium has at least two right angles
Kite doesn't come under both.
A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
Properties:
The two angles are equal where the unequal sides meet.
It can be viewed as a pair of congruent triangles with a common base.
It has 2 diagonals that intersect each other at right angles.
The longer or main diagonal bisects the other diagonal.
A kite is symmetrical about its main diagonal.
The shorter diagonal divides the kite into 2 isosceles triangles.
For images refer the attachment below.
Thank u.
Hope this helps you.
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