confidential1 good afternoon! today we will be learning about quadrilaterals and other polygons...
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CONFIDENTIAL 1
Good Afternoon!
Today we will be learning about Quadrilaterals and other polygons
(rectangle,square, rhombus, parallelogram,
trapezoid)Let’s warm up :
Angles of the triangle is given.What type of triangles are the following?
1) 53º, 55º and 72º.
2) 110º, 65º and 5º.
3) 26º, 90º and 64º.
4) 45º, 90º and 45º.
1) Acute triangle
2) Obtuse triangle
3) Right triangle
4) Right Isosceles triangle
CONFIDENTIAL 2
A triangle is one of the basic shapes of geometry: A polygon with three corners or vertices
and three sides or edges which are line segments.
We learnt about triangles.
The three angles always add to 180°.
vertex
arm
B
A
Ccb
a
angle ACBOr
angle c
Let’s review what we did in the last session
CONFIDENTIAL 3
Interior Angle: An Interior Angle is an angle inside a shape.
Interior Angle
Exterior Angle
45°135°
Exterior Angle: The Exterior Angle is the angle between any side of a shape, and a line extended from
the next side.
If you add up the Interior Angle and Exterior Angle you get a straight line, 180°.
Review
CONFIDENTIAL 4
The basic elements of any triangle are its sides and vertices. Triangles are classified depending on relative sizes of their
elements.
Triangles can be classified according to their internal angles.
Acute Triangle: An acute triangle is a triangle whose angles are all acute (i.e. less
than 90°).
B
A
Cc
ba
In the acute triangle shown above, a, b and c are all acute angles.
Triangle Classification
Review
CONFIDENTIAL 5
Right Triangle: A right triangle is a triangle with a right angle (i.e. 90°).
hypotenuse
The side opposite the right angle is always the triangle's longest side.It is called the hypotenuse of the triangle.
The other two sides are called the legs.
leg
leg
b°90°
a°
right angle
Review
CONFIDENTIAL 6
Obtuse Triangle: An obtuse triangle has one obtuse angle (i.e. greater than 90º).
The longest side is always opposite the obtuse angle.
In the obtuse triangle shown above, a is the obtuse angle.
>90°
a°
b°
Review
CONFIDENTIAL 7
The triangle classification is summarized as follows:
There are three special names given to triangles that tell how many sides (or angles)
are equal.
Equilateral Triangle: An equilateral triangle has all three sides equal in length. Its three
angles are also equal and they are each 60º.
a
aa
60º 60º
60º
Types of Triangles
Review
CONFIDENTIAL 8
Isosceles Triangle: An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal.
a a
xº xº
Scalene Triangle: A scalene triangle has no sides of equal length. Its angles are also all
different in size.
a
b
c
xº
yº
zº
Review
CONFIDENTIAL 9
Combining the Names
Right Isosceles Triangle:One right angle.Two equal sides.Two other equal angles always of 45°.
Right Scalene Triangle:One right angle.No equal sides.Two other unequal angles.
There are two types of right angled triangle:
Remember the little square in the triangle tells us that it is a right angled triangle.
Review
CONFIDENTIAL 10
Let’s start withQuadrilaterals and other polygons (rectangle,square, rhombus, parallelogram, trapezoid)
A polygon is a plane shape with straight sides.
Types of Polygons
Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself.
Simple Polygon
Complex
Polygon
CONFIDENTIAL 11
Concave or Convex: A convex polygon has no angles pointing inwards. More
precisely, no internal angles can be more than 180°.
If there are any internal angles greater than 180° then it is concave.
Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is
irregular .
convex Polygon
concave Polygon
regular Polygon
irregular Polygon
CONFIDENTIAL 12
Names of Polygons
Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
CONFIDENTIAL 13
There are many different kinds of quadrilaterals, but all have several things in common: all of them have
four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360
degrees.
But the sides have to be straight, and it has to be 2-dimensional.
We will learn about quadrilateral today.
A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a
pentagon is a 5-sided polygon, and so on.
CONFIDENTIAL 14
Types of Quadrilaterals
There are special types of quadrilateral :
the rectangle
the rhombus
the square
the kite
those are all parallelograms
CONFIDENTIAL 15
Also opposite sides are parallel and of equal length.
The Rhombus: A rhombus is a four-sided shape where all sides have equal length.
a
cbd
The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e.
90°).
CONFIDENTIAL 16
The Square: A Square is a four-sided shape which has all the sides equal and where every
angle is a right angle (i.e. 90°).
Also opposite sides of a square are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal
length).
CONFIDENTIAL 17
The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are
equal (angles "a" are the same, and angles "b" are the same).
a
b a
b
The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
A trapezoid is not a parallelogram because only one pair of sides is parallel.
CONFIDENTIAL 18
BREAK
CONFIDENTIAL 19
GAME
Click on the link below for some exciting puzzle
http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/010306snowman.html
CONFIDENTIAL 20
Assignments
Classify each quadrilaterals as rectangle,square, rhombus, parallelogram, trapezoid:
a
c b
d
ab
ab
1) 2)
3)
1) rhombus2) parallelogram
3) trapezoid
CONFIDENTIAL 21
Classify each quadrilaterals as rectangle,square, rhombus, parallelogram, trapezoid:
a
b
a
b
4) 5)
6) 7)
4) rectangle5) trapezoid
6) square7) parallelogram
CONFIDENTIAL 22
Write the given figure is a polygon or not a polygon.
8) 9)
10)
8) Polygon 9) Not a Polygon (has a curve)
10) Not a Polygon (open, not closed)
CONFIDENTIAL 23
A polygon is a plane shape with straight sides.
Types of Polygons
Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!
Simple Polygon
Complex
Polygon
Very Good!Let's Review
CONFIDENTIAL 24
Concave or Convex: A convex polygon has no angles pointing inwards. More
precisely, no internal angles can be more than 180°.
If there are any internal angles greater than 180° then it is concave.
Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is
irregular .
convex Polygon
concave Polygon
Regular Polygon
Irregular Polygon
CONFIDENTIAL 25
Names of Polygons
Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
CONFIDENTIAL 26
There are many different kinds of quadrilaterals, but all have several things in common: all of them have
four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360
degrees.
But the sides have to be straight, and it has to be 2-dimensional.
A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a
pentagon is a 5-sided polygon, and so on.
Review
CONFIDENTIAL 27
Also opposite sides are parallel and of equal length.
The Rhombus: A rhombus is a four-sided shape where all sides have equal length.
a
cbd
The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e.
90°).
Review
Types of Quadrilaterals
CONFIDENTIAL 28
The Square: A Square is a four-sided shape which has all the sides equal and where every
angle is a right angle (i.e. 90°).
Also opposite sides of a square are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal
length).
Review
CONFIDENTIAL 29
The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are
equal (angles "a" are the same, and angles "b" are the same).
a
b a
b
The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
A trapezoid is not a parallelogram because only one pair of sides is parallel.
Review
CONFIDENTIAL 30
You have done a nice job.See you in the next session.
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