1. Today we will be learning about
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) Acute triangle
1) º, 55º and 72º.
2) Obtuse triangle
2) º, 65º and 5º.
3) Right triangle
3) º, 90º and 64º.
4) º, 90º and 45º.
4) Right Isosceles triangle
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2. We learnt about triangles.
Let’s review what we did in the last session
We learnt about triangles.
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. B A C c b a
angle ACB Or
angle c
vertex
arm
The three angles always add to 180°.
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3. Interior Angle: An Interior Angle is an angle inside a shape.
Review
Interior Angle: An Interior Angle is an angle inside a shape.
Exterior Angle: The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.
Exterior Angle
135°
Interior Angle
45°
If you add up the Interior Angle and Exterior Angle you get a straight line, 180°.
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4. Triangle Classification
Review
Triangle Classification
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 C c b a
In the acute triangle shown above, a, b and c are all acute angles.
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5. It is called the hypotenuse of the triangle.
Review
Right Triangle: A right triangle is a triangle with a right angle (i.e. 90°).
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. b°
90° a°
hypotenuse
leg
right angle
leg
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6. The longest side is always opposite the obtuse angle.
Review
Obtuse Triangle: An obtuse triangle has one obtuse angle (i.e. greater than 90º).
The longest side is always opposite the obtuse angle.
>90° a° b°
In the obtuse triangle shown above, a is the obtuse angle.
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7. Review
Types of Triangles
There are three special names given to triangles that tell how many sides (or angles) are equal.
The triangle classification is summarized as follows:
Equilateral Triangle: An equilateral triangle has all three sides equal in length. Its three angles are also equal and they are each 60º. a
60º
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8. Review
Isosceles Triangle: An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal. a 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
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9. Combining the Names Right Isosceles Triangle: One right angle.
Review
Combining the Names
There are two types of right angled triangle:
Right Isosceles Triangle:
One right angle.
Two equal sides.
Two other equal angles always of 45°.
Right Scalene Triangle:
No equal sides.
Two other unequal angles.
Remember the little square in the triangle tells us that it is a right angled triangle.
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10. Quadrilaterals and other polygons (rectangle,
Let’s start with
Quadrilaterals 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
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11. If there are any internal angles greater than 180° then it is concave.
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.
convex Polygon
concave Polygon
Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular .
regular Polygon
irregular Polygon
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12. Names of Polygons Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
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13. 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.
But the sides have to be straight, and it has to be 2-dimensional.
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.
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14. Types of Quadrilaterals
There are special types of quadrilateral :
the rectangle
the rhombus
the square
the kite
those are all parallelograms
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15. Also opposite sides are parallel and of equal length.
The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e. 90°).
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 c b d
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16. Also opposite sides of a square are parallel.
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).
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17. NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
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
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.
A trapezoid is not a parallelogram because only one pair of sides is parallel.
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18. BREAK
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19. Click on the link below for some exciting puzzle
GAME
Click on the link below for some exciting puzzle
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20. Assignments Classify each quadrilaterals as rectangle,
square, rhombus, parallelogram, trapezoid: 1) 2) a c b d a b
1) rhombus
2) parallelogram 3)
3) trapezoid
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21. Classify each quadrilaterals as rectangle,
square, rhombus, parallelogram, trapezoid: 4) 5)
4) rectangle
5) trapezoid a b 6) 7)
7) parallelogram
6) square
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22. Write the given figure is a polygon or not a polygon.8) 9)
8) Polygon
9) Not a Polygon (has a curve)
10)
10) Not a Polygon (open, not closed)
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23. A polygon is a plane shape with straight sides.
Very Good!
Let's Review
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
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24. If there are any internal angles greater than 180° then it is concave.
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.
convex Polygon
concave Polygon
Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular .
Regular Polygon
Irregular Polygon
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25. Names of Polygons Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
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26. But the sides have to be straight, and it has to be 2-dimensional.
Review
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.
But the sides have to be straight, and it has to be 2-dimensional.
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.
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27. Types of Quadrilaterals
Review
Types of Quadrilaterals
The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e. 90°).
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 c b d
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28. Also opposite sides of a square are parallel.
Review
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).
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29. NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Review
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
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.
A trapezoid is not a parallelogram because only one pair of sides is parallel.
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30. See you in the next session.
You have done a nice job.
See you in the next session.
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