QUADRILATERALS Mathematics - Class 8 Chapter 3 Unit 5
Jan 13, 2016
QUADRILATERALSMathematics - Class 8
Chapter 3 Unit 5
Module Objectives• Learn to identify quadrilaterals• Understand basic properties of quadrilaterals• Classify quadrilaterals into common types,
and recognize their specific properties
Basic Geometrical Figures• Line
• Bounded by 2 end points• All points are collinear i.e. lie on the same straight line
• Triangle• Plane figure bounded by three sides• Atleast 3 non-collinear points
• Quadrilateral• ‘Quad’ = four, ‘lateral’ = side• Formed by joining 4 points• Any 3 out of these 4 points are non-collinear
Quadrilaterals• Any closed figure having four sides formed by
joining four points and three of which are not collinear is called quadrilateral.
A
C
BD
P
Q
R
S
W
YZ
X
M
OP
N
Are these Quadrilaterals?
No, the sides cross each other
A
B
CD
A
B
C D
No, the sides are all not line segments
A
C
BD
Yes, it is a closed figure •formed by the union of four line segments •that join 4 points lying on the same plane•no three of which are collinear •and each segment meet exactly 2 other lines, each at their end point
Quadrilateral Notations• Let ABCD be a quadrilateral
• Vertices - Points A, B, C and D• Four sides - Segments AB, BC, CD and DA• Four angles - DAB, ABC, BCD and CDA• Two diagonals - Segments AC and BD
A
C
BD
• Naming Hint: If you join adjacent letters in the name, then there should not be any crossing of line segments
• Naming a quadrilateral e.g. ABCD• Refer to its vertices in a particular order• We cannot read it as ADBC or ADCB
Quadrilateral Notations• Adjacent or consecutive sides• Two sides of a quadrilateral have a
common end point• E.g. AB and AD, CD and CB
• Opposite sides• Two sides do NOT have a common end
point• E.g. AB and DC
A
C
BD
Quadrilateral Notations• Adjacent or consecutive angles• Two angles have a side common to
them• E.g. DAB and ABC, with AB being
the common side
• Opposite angles• Two angles do NOT have a common
side• E.g. DAB and ABC
A
C
BD
Properties of Quadrilaterals• Diagonal Property• Diagonal AC divides the quadrilateral
into 2 triangles ABC and ADC
• Angle Sum Property• The sum of the angles of a
quadrilateral is 360• ABC + BCD + CDA + DAB = 360
D
B
CA
A
C
BD
Types of Quadrilaterals• Convex Quadrilateral• Quadrilateral in which every
internal angle of the quadrilateral is lesser than 180.
• Concave Quadrilateral• A quadrilateral is concave if any
internal angle of the quadrilateral is greater than 180.
N
L
MK
P
Q
R
S
Special Kinds of Quadrilaterals• Classification based on nature of sides or angles
• Is Parallelogram a type of Trapezium? • Yes, it has parallel opposite sides
• Is Kite a type of Parallelogram?• No, it does not have 2 pairs of equal-length opposite sides
Type of Quadrilateral
Properties
Trapezium One pair of opposite sides are parallel
Parallelogram Both pairs of opposite sides are parallelOpposite sides are equal and opposite angles are equal
Kite Two pairs of equal-length adjacent sides
Trapezium
• Quadrilateral with a pair of opposite side that are parallel
• Isoceles Trapezium• Non-parallel sides are equal• Base angles are equal• Diagonal are equals• Adjacent angles corresponding to
parallel sides are supplementary
Parallelograms
• Both pairs of opposite sides are parallel
• Opposite sides are of equal length
• Special Kinds of Parallelograms• Rectangles• Rhombus• Square
W
YZ
X
Kinds of Parallelograms - Rectangle
• All angles are equal and right angles
• All sides are not equal• Diagonals are equal and
bisect each other
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ά
ά
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Kinds of Parallelograms - Rhombus
• All sides are equal• All angles are not equal• Diagonals bisect each other at
right angles• Two diagonals divide the
rhombus into four congruent right angled triangles
• Angles are bisected by the diagonals
D
C
B
A
Kinds of Parallelograms - Square• Square• All its angles are equal and right
angles• All sides are equal• Both diagonals are equal• Diagonals bisect each other at
right angles
Kind of ParallelogramsParallel Sides All Sides All Angles Diagonals
Rectangle2 pairs of opposite sides
Equal Equal &Right angles
Equal &Bisect each other
Rhombus Equal Not equal Bisect each other at right angles
Square Equal Equal
Kite
• Type of quadrilateral but not a parallelogram
• Has 2 pairs of equal-length adjacent sides
• Two isoceles triangles are joined along the common base
• Rhombus is a special kind of Kite
A
ODB
C