Special types of quadrilaterals

1. Mathematics
Parallelograms

2. Contents
Contents
Special
Quadrilaterals
Properties of a
Parallelogram
Diagonal
Properties of a
Rectangle &
Rhombus
Properties of a
Square, Kite &
Isosceles
Trapezium

3. 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.

4. 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

5. 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

6. 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
A
B

7. Relation of Parallelograms
Quadrilaterals
Parallelograms
Rectangle
Square
Rhombus
Kite Arrowhead
Trapezium
Isosceles
Trapezium
Family Tree

8. 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.

9. Picture of Parallelogram
A B
D C
O

10. 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.

11. 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.

12. Picture of Rectangle
A B
D C
O

13. 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.

14. Picture of Rhombus
A B
D C
O
x
y
b
a

15. Diagonal Properties of a Square
Properties of
a Square
Parallelogram
It has all
properties of a
parallelogram.
Angles
All angles are
= 90◦
Diagonals
The diagonals
are equal and
bisect each
other at right
angles.
The bisected
angle will be
then 45◦.
A parallelogram in
which all 4 sides are
equal and 4 angles are
equal (90◦ each) is a
square.

16. Picture of Square
45◦
45◦
45◦
45◦
A B
D C
O

17. Diagonal Properties of a Kite
Properties of a Kite
Diagonals
Diagonals are
perpendicular to
each other.
Angles
Opposite angles are
equal.
Sides
Horizontal Diagonal
(when in 2 halves)
are equal to each
other.
Bisection
In 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.

18. Picture of Kite
Angle A= Angle C
OA= OC
AC perpendicular to
BD
A
B
C
D
O

19. Diagonal Properties of an I. Trapezium
Properties of a I.
Trapezium
Diagonals
The diagonals are
always equal.
Co-Interior Angles
The co-interior
angles are always
supplementary.
Angles
Angles above are
equal. Angles below
are equal.
Bisection
In 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.

20. Picture of Isosceles Trapezium
A B
D C
u z
x y

21. Thank You
•By Group 3
•Have a nice
day.
Knowledge is Power