Quadrilaterals – Properties of Plane Shapes

A quadrilateral is a four-sided plane shape with four angles and the sum of all the angles is 360°.

A diagonal is a straight line that connects the opposite corners of a quadrilateral. There are two diagonals and they divide a quadrilateral into two triangles. Each triangle has an angle sum of 180°. Therefore, the total angle sum of the quadrilateral is 360°.

Types of Quadrilaterals:

1. Parallelogram
2. Rhombus
3. Rectangle
4. Square
5. Trapezium
6. Kite

Parallelogram:

i. A parallelogram is a quadrilateral that has two opposite sides parallel and equal in length.

ii. The opposite angles are equal.

iii. Sum of angles in a parallelogram is 360°

iv. The diagonals bisectBisect means dividing into two equal parts. It means to divide a geometric figure such as a line, an angle or any other shape into two congruent parts (or two parts... More each other but are unequal in a parallelogram

Rhombus:

i. A rhombus is a quadrilateral that has all four sides equal in length

ii. Opposite sides are parallel and opposite angles are equal.

iii. In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°).

iv. The diagonals bisect the angles.

v. The diagonals are unequal.

Rectangle:

i. A rectangle is a quadrilateral that has opposite sides equal and each angle is 90°.

ii. The opposite sides are parallel. 

iii. The diagonal lines are equal and bisect each other

iv. Each diagonal divides the rectangle into two equal shapes, namely a right-angled
triangle.

iv. Intersection point of the diagonals is called the centre of the rectangle

v. A rectangle can be a parallelogram, rhombus or square.

Square:

i. A square is a quadrilateral that has all its sides equal and each angle is 90°. 

ii. The opposite sides are parallel.

iii. Diagonals are equal in length and bisect each other at 90°.

iv. Squares are parallelograms that are both rectangles and rhombuses, i.e. all four angles are right angles (90°) and all sides are equal.

Trapezium:

A trapezium is a quadrilateral with one pair of opposite sides parallel. The diagonals are unequal.

• When the two non-parallel sides are equal in length it is called an isosceles trapezium.

• Right-angled trapeziums are trapeziums with two adjacent right angles.

• A trapezium with all the sides not equal is called a scalene trapezium. In a scalene trapezium, no two angles are equal.

Kite:

i. A kite is a quadrilateral that has two pairs of adjacent sides equal in length and one pair of opposite angles equal.

ii. The diagonals are unequal.

Note: (i) The diagonals are equal in a square, a rectangle and an isosceles trapezium.
(ii) The diagonals are unequal in a parallelogram, a rhombus, a trapezium and a kite.