Mathematics presentation2
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Transcript of Mathematics presentation2
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