Modulepolygons

Prepared By: Prepared By: Norisah Bt MustaffaNorisah Bt MustaffaKOSPINTKOSPINT

20th June 2003

Polygons Triangles

Quadrilateral

Glossary

Click For L

esson PolygonsPolygonsSymmetry

Recognizing Polygons Naming Polygons Determining The Number Of Sides, Vertices, And

Diagonals Of Given Polygons Sketching Polygons Determining And Drawing Lines Of Symmetry Completing Shapes, Given Part Of The Shapes And Lines

Of Symmetry Drawing Triangles and Quadrilateral Geometric Properties of Triangles and

Quadrilateral Glossary Exercise

Quick Exercise

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PolygonsPolygons

A polygon is a closed diagram in two-dimensional shape that is bound by three or more straight lines.

three sided shapesthree sided shapes

10.1 Recognizing Polygons

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four sided shapesfour sided shapes

Recognising PolygonsPolygonsPolygons

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five sided shapesfive sided shapes


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six sided shapessix sided shapes

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seven sided shapesseven sided shapes


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Recognising PolygonsNow you know what polygons are. Can you sketch eight sided shapes polygon?

Do you know what the different types of polygons are called?

PolygonsPolygons

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Are these shapes polygons?


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PolygonsPolygons

These shapes are not polygons. They have no straight lines and are not closed diagrams.

Recognising Polygons

Not straight lines.

Not all sides have straight lines.

Not closed diagrams

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PolygonsPolygonsNaming PolygonsWe name polygons according to the number of sides the polygons have.Look at the table below.

Pentagon

Quadrilateral

Triangle

NamePolygon

Octagon

Heptagon

Hexagon

NamePolygon

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PolygonsPolygonsSides of Polygons

Side

Side is a line which is part of a polygon

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PolygonsPolygonsVertices of Polygons

VertexThe vertex of a polygon is the meeting point of two sides.

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PolygonsPolygonsDiagonals of Polygons

Diagonals

A diagonal is a straight line that joins two non-adjacent vertices. How many diagonals in a quadrilateral?

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PolygonsPolygonsTo Find The Number of Diagonals in a Polygon

A pentagon has 5 diagonals

1

3

2

2 diagonals can be formed


1 diagonal can be formed

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PolygonsPolygonsTo Find The Number of Diagonals In A Polygon

An octagon has 20 diagonals

1

2

3

4





2 diagonals can be formed1 diagonal can be formed

6

5

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Sketching PolygonsPolygonsPolygons

We have to know the number of sides or vertices that the polygon has, to sketch a polygon. Label the polygon drawn by using the capital letters to name the vertices.1) Sketch a triangle on dotted grids. Name the vertices of this polygon.

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

A

BC

Are the number of sides and the number of vertices of a polygon are the same?

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PolygonsPolygons

A shape has symmetry if it can be divided equally. So, that one half fit exactly onto the other. This shape is called symmetrical shape.

10.2 Symmetry: Determine and Drawing

Lines of symmetry(2 lines of symmetry)

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PolygonsPolygons


Symmetry: Determining and Drawing

Line of symmetry(One line of symmetry

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PolygonsPolygons


Symmetry: Determine and Drawing

No line of symmetry.Shapes which are not

symmetrical are called asymmetrical shapes

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PolygonsPolygons

A symmetrical shape has a line or lines symmetry. When the shape is folded along the line of symmetry, one part of the shape overlaps exactly onto the other part.

Symmetry: Determine and DrawingCan you determine the symmetry shape on the diagrams below?

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PolygonsPolygonsCompleting Symmetrical ShapesWe can complete the shape when part of a symmetrical shape and the line (s) of symmetry are given.

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PolygonsPolygons10.3 TRIANGLESA triangle can be drawn by using a protractor and ruler when,(a) the lengths of all the sides are given.(b) two angles and a side are given(c) two sides and an angle are given.

(b)

3cm

50º

50º

P Q

R

50ºK

(c)70º

4cm

7cm

J

L

(a)5cm4cm

6cm

A

B C

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PolygonsPolygonsDrawing Triangles

Solution:Step 1: Make a sketch of ABC

60° 60°A B

C

6cm

Example: Draw a triangle with the given measurements. AB=6cm, A=60°, B=60°

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PolygonsPolygonsDrawing TrianglesStep 2: Draw AB=6cm using a pencil and a ruler.

A B6cm

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165°

150°

135°

120° 105°

90°75°

15°

30°

45°

60°

0° 180°180°

165°

150°

135°

120°105° 75°

60°

45°

30°

15°

90°

0°


A B60°

6cm

Step 3: Use a protractor to draw A = 60°

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165°

150°

135°

120° 105°

90°75°

15°

30°

45°

60°

0° 180°180°

165°

150°

135°

120°105° 75°

60°

45°

30°

15°

90°

0°


A B60°

6cm60°

Step 4: Use a protractor to draw B = 60°

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PolygonsPolygonsDrawing TrianglesStep 5: Point C is a intersection of the two lines drawn.

A B60°

C

6 cm60°

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PolygonsPolygonsSymmetry of Triangles

Triangles with sides of different lengths has different number of

lines of symmetry.

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PolygonsPolygonsGeometric Properties of Different Types of Triangles Triangles are named based on their geometric properties. We can classify triangles into three types based on the length of their sides.Equilateral

Triangle

All sides are of equal length

Isosceles Triangle

Two of its sides are of

equal length.

Scalene Triangle

All sides are of different

length.

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PolygonsPolygonsGeometric Properties of Different Types of Triangles Triangles also can be classified based on the size of the angles of the triangles.

Acute TriangleAll the angles

are acute angles.

Right Angled TriangleOne of its angle is

a right angle.

Obtuse Triangle

One of its angle is

an obtuse angle.

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PolygonsPolygonsSolving Problems Involving Triangles The sum of the angles of a triangle is 180°.

a b

c p

q ra + b + c = 180°a = b = c = 60°

p + q + r = 180°q = 90°p + r = 90°

x + y+ z = 180°x = y

x y

z

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PolygonsPolygonsSolving Problems Involving Triangles

In the figure below, find the value of x.

48°

x

R

P QS

Solution: Q= P=48° (Isosceles triangle) S = 90°The sum of the angles of a triangle is 180°.So, x = 180° - 90° - 48° = 42°

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PolygonsPolygons10.4 QUADRILATERALS

Quadrilaterals are polygons

with four sides. A

quadrilateral has four

vertices and two diagonals.

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PolygonsPolygonsQUADRILATERALSDetermining and Drawing Lines of Symmetry of Quadrilaterals

side

diagonals

line of symmetry

vertex

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PolygonsPolygonsQUADRILATERALSDetermining and Drawing Lines of Symmetry of Quadrilaterals

4 lines of symmetry 2 lines of symmetry no line of symmetry

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PolygonsPolygonsDrawing QuadrilateralQuadrilateral can drawn using a ruler and a protractor when three sides and two angles are given. Example: Draw ABCD below to scale using a ruler and protractor.

A B

D C6 cm

3 cm

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PolygonsPolygonsDrawing QuadrilateralStep 1: Draw a 6 cm line using a ruler and pencil. Name the line AB

A B6 cm

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165°

150°

135°

120° 105°

90°75°

15°

30°

45°

60°

0° 180°180°

165°

150°

135°

120°105° 75°

60°

45°

30°

15°

90°

0°

PolygonsPolygonsDrawing QuadrilateralStep 2: Use a protractor to draw perpendicular lines from points A and B.

A B6 cm

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165°

150°

135°

120° 105°

90°75°

15°

30°

45°

60°

0° 180°180°

165°

150°

135°

120°105° 75°

60°

45°

30°

15°

90°

0°

PolygonsPolygonsDrawing QuadrilateralStep 3: Use a protractor to draw perpendicular lines from points A and B

A B6 cm

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PolygonsPolygonsDrawing QuadrilateralStep 4: Use a ruler mark points C and D which are 3 cm from B and A.

A B

D C

6 cm

3 cm3cm

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PolygonsPolygonsDrawing QuadrilateralStep 5: Join points C and D with a straight line using a ruler. The line CD should be 6 cm in length.

A B

D C6 cm

6 cm

3 cm3 cm

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PolygonsPolygonsDrawing QuadrilateralStep 6: Complete the figure.

A B

D C6 cm

3 cm

6 cm

3 cm

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*All sides are equals. *Opposite sides are parallel*Each angle is 90°-4 lines of symmetry*Opposite sides are equal and parallel*Each angle is 90°-2 lines of symmetry*Opposite sides are equal and parallel-no line of symmetry

PolygonsPolygonsGeometric Properties of Different Types of Quadrilaterals.

Square

Rectangle

Parallelogram

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*All sides are equals. *Opposite sides are parallel*Opposite angles are equal in size-2 lines of symmetry

*Has one pair of parallel opposite sides which do not have the same length-no line symmetry.

PolygonsPolygonsGeometric Properties of Different Types of Quadrilaterals.

Trapezium

Rhombus

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PolygonsPolygonsSolving Problems Involving QuadrilateralsThe sum of the angles of a quadrilateral is

360°.

a+b+c+d = 360°

a+b+c+d=360°

a=c, b=d.

a+b+c+d=360°

a

b c

da b

cd

a b

cd<<<<

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PolygonsPolygonsSolving Problems Involving QuadrilateralsCalculate the value of x in the diagram below.

Solution:x+x+58°+62° = 360°2x = 360°- 58°- 62° = 240°x = 240° ÷ 2 = 120°

x x

62°58°

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GlossaryItem Description

Acute Angle

An angle that is less than 90°

Acute Triangle

A triangle with all three inside being acute

Adjacent Next toAngle An amount of turn measured in

degreesClosed diagram

A diagram of figure whose sides begin and at the same point

Degree A unit for measuring anglesEquilateral triangle

A triangle has three sides of equal length and each angle is equal to 60°

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Figure Another name of a number, digit, line, shape or object.

Geometric properties

Characteristic of a figure or solid based on regular lines or shapes.

Heptagon A polygon with seven sidesHexagon A polygon with six sidesIntersecting line

Lines that cut across or cross each other

Isosceles triangle

A triangle with two equal sides

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Line A long thin mark drawn on a surface. It can be straight or curved. It has no thickness and no dimension.

Line of symmetry

The line which divides something in half so that one half is exactly the same as the other half .

Obtuse angle

An angle greater than a right angle (90°) but less than the angle the angle of a straight line (180°)

Octagon A polygon with eight sides.Parallel lines

Two or more lines that go in exactly the same direction and are at the same distance apart at every point, so the lines never meet.

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Parallelogram

A plane figure with four sides, having parallel and equal opposite sides.

Pentagon A polygon with five sidesPerpendicular lines

Lines that intersect to make right angles.

Polygon A plane shape or a closed figure with three or more straight sides.

Protractor An instrument used to measure and draw angles.

Quadrilateral

A plane figure or shape having four sides.

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Rectangle A four-sided polygon with two pairs of equal and parallel sides and four right angles.

Reflex angle

An angle greater than the angle of a straight line (180°) but less than one whole turn or revolution

Rhombus Parallelogram with four equal sides.Right angle An angle measuring exactly 90°.Right-angle triangle

A triangle with a right angle.

Scalene triangle

A triangle with each side different in length.

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Shape The outer form of a figureSketch A simple quickly-made drawing that

does not show much detail.Square A quadrilateral having four equal

sides and four right angles.Symmetry Similarity of form on either side of a

dividing line.Trapezium A plane figure with four sides where

one pair of sides is parallel and the other pair is not.

Triangle A polygon with three sides.

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Vertex The point where two adjacent lines meet to form an angle, where three of more edges meet to form a corner.

Vertically opposite angles

When two lines intersect, they form four angles at the vertex. The angles opposite each equal in size and are called vertically opposite angles

Vertices The plural of vertex.

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Quick Exercise

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