Mathematics

Parallelograms

Contents

Contents

Special Quadrilaterals

Properties of a Parallelogram

Diagonal Properties of a

Rectangle & Rhombus

Properties of a Square, Kite &

Isosceles Trapezium

Definition of Parallelograms?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Special Quadrilaterals

Special Quadrilaterals Figure

Parallelogram A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

D C Parallelogram ABCD (AB||DC, AD||BC)

Rectangle A parallelogram in which all four angles are right angles is a rectangle.

D C Rectangle ABCD (AB=DC, AD=BC) Each int. angle=90◦

Rhombus A parallelogram whose all four sides are equal is a rhombus.

D C Rhombus (AB=BC=CD=DA)

A B

A B

A B

Special Quadrilaterals (Continued)

Special Quadrilaterals Figure

Square A parallelogram in which all 4 sides are equal and 4 angles are equal (90◦ each) is a square.

D C Square ABCD (AB=BC=CD=DA) Each angle 90◦

Trapezium A quadrilateral with exactly 1 pair of parallel sides is a trapezium.

D C Trapezium ABCD (AB||DC, AD||BC)

Isosceles Trapezium A trapezium in which 2 non parallel sides are equal. Each pair of base angles are equal. This is an isosceles trapezium.

D C I. Trapezium ABCD (AB||BC, AD=BC)

A B

A B

A B

Special Quadrilaterals (Continued)

Special Quadrilaterals Figure

Kite A quadrilateral in which 2 pairs of adjacent sides are equal is a kite.

D Kite ABCD C (AB=BC, AD=DC) (AB=CD, BC=AD)

Arrowhead A kite with one reflex angle is called an arrowhead.

D Trapezium ABCD (AB||DC, AD||BC)

C

A

B

AB

Relation of Parallelograms

Quadrilaterals

Parallelograms

Rectangle

Square

Rhombus

Kite Arrowhead

Trapezium Isosceles Trapezium

Family Tree

Properties of a Parallelogram

Properties

Diagonals

Each diagonal divides into

two congruent triangles.

Sides

The opposite sides of a

parallelogram are equal.

Angles

The opposite angles of a

parallelogram are equal.

Bisection

The diagonals of a

parallelogram bisect each

other.

A parallelogram is a quadrilateral with both pairs of opposite sides

parallel.

Picture of Parallelogram

A B

D C

O

A quadrilateral is a parallelogram.

If the opposite sides are equal.

If opposite angles are equal.

If its diagonal bisect each other.

If it has one pair of opposite sides parallel and equal.

The Converse

The Converse of the properties for parallelograms is also true.

Diagonal Properties of a Rectangle

Properties of a Rectangle

Parallelogram

It has all properties of a parallelogram.

Angles

All angles of a rectangle are right angles.

Diagonals

The diagonals of the rectangle

are equal.

A rectangle is a parallelogram with the opposite sides equal in terms of size. All angles are 90◦. This shape itself is a rectangle.

Picture of Rectangle

A B

D C

O

Diagonal Properties of a Rhombus

Properties of a Rhombus

Parallelogram

It has all properties of a parallelogram.

Angles

Opposite angles of a rhombus

are equal.

Diagonals

Diagonals of a rhombus bisect

each other at 90◦

A parallelogram whose all four sides are equal is a rhombus.

Picture of Rhombus

A B

D C

O

xy

ba

Diagonal Properties of a Square

Properties of a Square

Parallelogram

It has all properties of

a parallelogra

m.

Angles

All angles are = 90◦

DiagonalsThe diagonals are equal and

bisect each other

at right

angles.

The bisecte

d angle will be then 45◦.

A parallelogram in which all 4 sides are equal and 4 angles are equal (90◦ each) is a square.

Picture of Square

45◦

45◦

45◦

45◦

A B

D C

O

Diagonal Properties of a Kite

Properties of a KiteDiagonals

Diagonals are perpendicular to each other.

AnglesOpposite angles are equal.

SidesHorizontal Diagonal (when in 2 halves)

are equal to each other.

BisectionIn a kite ABCD, diagonal BD will bisect

angle B and D.

A quadrilateral in which 2 pairs of

adjacent sides are equal is a kite.

Picture of Kite

Angle A= Angle COA= OC

AC perpendicular to BD

A

B

C

D

O

Diagonal Properties of an I. Trapezium

Properties of a I. TrapeziumDiagonals

The diagonals are always equal.

Co-Interior AnglesThe co-interior angles are always

supplementary.

AnglesAngles above are equal. Angles below

are equal.

BisectionIn a kite ABCD, diagonal BD will bisect

angle B and D.

A trapezium in which 2 non parallel sides are

equal. Each pair of base angles are equal. This is an isosceles trapezium.

Picture of Isosceles Trapezium

A B

D Cu z

x y

Thank You•By Group 3

•Have a nice day.

Knowledge is Power