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Lets review what we have learned

Polygons: A polygon is a closed plane figure made up of 3 or more line segments.

Types of Polygons:

Concave, Convex, Regular and Irregular.

Names of Polygon according to the sides are Triangles, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon and Decagon.

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State True/ False

Warm up

1. The shape with three or more sides is a polygon True

2. Hexagon has the maximum number of sides. False

3. There are 20 diagonals in a Decagon. True

Fill in the blanks:

1. ________ is not an irregular polygon Square

2. Nonagon has________ sides. 9

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Formulae

Sum of Interior Angles= 180(n-2), n denotes

the number of sides

Each interior angle of a regular polygon = 180(n-2) where n represents number of sides. n

Each exterior angle (regular polygon) = 360 , where n represents number of sides. n

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Lets get startedLets get startedTriangle:- A three-sided polygon is called to be a

triangle.

The sum of all angles in a triangle is 180 degrees.

Triangles can be classified according to the length of their sides and the size of their angles.

A

B C

side

1

side 2

sidde 3

Angle A + Angle B + Angle C = 180 degrees

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Classifying Triangles according to the Length of their Sides

Scalene Triangles

Equilateral Triangles

Isosceles Triangles

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Scalene TrianglesScalene Triangles

A scalene triangle has no equal sides. Its angles are also all different in size.

In DEF, the sides are a, b and c. Angles are x , y and z.

ab

c

x

y z

D

E F

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Equilateral Equilateral TrianglesTriangles

An equilateral triangle has all three sides equal in length. Its three angles are also equal and they are each 60 degrees.

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Isosceles TrianglesIsosceles Triangles

An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal.

a a

x x

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Classifying Triangles according to the Length of their Angles

Acute-angled Triangles

Obtuse-angled Triangles

Right-angled Triangles

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Acute-angled Acute-angled TriangleTriangle

An acute angle is an angle whose measure is greater than 0° and less than 90º. An acute triangle is a triangle whose angles are all acute . In the acute triangle shown below, a,b and c are all acute angles.

a

c

b

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Obtuse-angled Obtuse-angled TriangleTriangle

An obtuse angle is an angle whose measure is greater than 90º and less than 180º. An obtuse triangle has one obtuse angle. The longest side called the hypotenuse is always opposite the obtuse angle.

aLongest

side

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Right-angled Right-angled TriangleTriangle

A right-angled triangle has one angle equal to 90°. That is, one angle is a right angle . 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.

90

legs

legs

hypotenuse

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ExampleExampleName the following triangles:

2)

1) Isosceles

triangle

Draw a square around the right triangle:

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Your turnYour turnIdentify the following types of triangles:

1) ___- a triangle with no equal sides. Scalene triangle2) ____- a triangle with a right angle. Right Triangle3) _____- a triangle with at least two sides equal. Isosceles

triangle 4) _____- a triangle with three acute angles. Acute Triangle5) ____- a triangle with three equal sides. Equilateral Triangle

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Quadrilateral

A four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees. The figure represents the types of quadrilaterals.

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Quadrilaterals Family

TRAPEZOID

Trapezoid is a quadrilateral with only one pair of parallel sides. In regular trapezoid, base angles are equal.

Base

Opposite side

Base Angle

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PARALLELOGRAMPARALLELOGRAM

Opposite sides of a parallelogram are parallel and equal in length. Opposite angles are equal in size. Diagonals (AC & BD) bisect each other. Diagonals form 2 congruent triangles

In Parallelogram ABCD, the sides AB and CD are equal. ▪, ● denotes the equal angles.

A

CD

B▪

▪●

●

Note: Rectangles and squares are special kinds of parallelograms.

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RHOMBUSRHOMBUS

All sides of a rhombus are equal in length Opposite sides are parallel. Opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each other at

right angles.

AB , CD &

AD, BC are parallel.

Angle B = Angle D

Angle A= Angle CNote: A parallelogram with four equal sides is called a rhombus.

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RECTANGLERECTANGLE

Opposite sides of a rectangle are parallel and equal in length.

All angles are equal to 90°.

A B

CD

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SQUARESQUARE Opposite sides of a square are parallel and all

sides are equal in length.

All angles are equal to 90°.

A B

CD

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ExampleExample

1)A rectangle has ____ pairs of parallel sides. Two

2)In a parallelogram any two opposite angles are _____. Equal

3) The sum of the angles of a quadrilateral is _____ degrees. 360

4) In ________ trapezoid, base angles are equal. Regular

5) Name the quadrilateral whose angles are 90 degree. Square

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Your TurnYour Turn

1. One of these is not a quadrilateral. Triangle(trapezoid, square, triangle, rectangle)2. Write True or False. Rectangles and Squares are special kinds ofParallelograms. True3. A quadrilateral with only 1 pair of parallel sides is called________. Trapezoid4. What is a parallelogram with 4 right angles and 2 pairsof equal sides. Rectangle5. Example of quadrilateral is ______. Rhombus(Rhombus, triangle)

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BREAK TIME!!!!

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LETS PLAY A GAME

Click Here to Play

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Calculate the size of the missing angle in the following triangle.

80

48

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Find the angle x in the given diagram.

A B

C

D

68

126

106

x

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The opposite sides of a parallelogram are represented by 2x+10 and 5x-20.Find the length of the side of the parallelogram represented by 4x-1.

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Lets review what we have learned in our lesson

Triangle: Three sided polygon.

Types of Triangles: Triangles can be classified according to the length of their sides and the size of their angles.

1)Scalene Triangle

2)Isosceles Triangle

3)Equilateral Triangle

1)Acute-angled Triangle

2)Obtuse-angled Triangle

3)Right-angled Triangle

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Quadrilateral: Four sided polygon.

Types of Quadrilateral:

1)Trapezoid - a quadrilateral with two parallel sides.

2)Rhombus - A quadrilateral with four equal sides and opposite angles equal.

3)Parallelogram - Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other.

4)Rectangle - A parallelogram in which all angles are right angles.

5)Square – It is a special case of a rectangle as it has four right angles and parallel sides.

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Sum of angles in a triangle

= 180 degrees

Sum of angles in a Quadrilateral

= 360 degrees

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Calculate the size of the missing angle in the following triangle.

80

48

Solution:

Let the missing angle be x.x + 80+48 = 180 (Angle sum of a triangle is 180) x + 128 = 180x + 128 - 128 = 180 -128 x = 52 So, the missing angle is 52

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Find the angle x in the given diagram.

A B

C

D

68

126

106

x

Solution:

x + 68 +126 + 106 = 360 (Angle of a quadrilateral =360) x + 300 = 360 (Subtract 300 from both sides) x + 300 – 300 = 360 – 300 x = 60

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The opposite sides of a parallelogram are represented by 2x+10 and 5x-20.Find the length of the side of the parallelogram represented by 4x-1.

The Opposite sides of parallelogram are equal. 2x +10 = 5x – 20 ( solve for x) 10 + 20 = 5x – 2x 30 = 3x divide by 3 on both sides x = 10

4x – 1 => 4(10) -1 = 40 – 1 = 39

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Lets review what we have learned in our lesson

Triangle: Three sided polygon.Types of Triangles: Triangles can be classified according to the length of their sides and the size of their angles.

1)Scalene Triangle

2)Isosceles Triangle

3)Equilateral Triangle

1)Acute-angled Triangle

2)Obtuse-angled Triangle

3)Right-angled TriangleSum of angles in a triangle = 180 degrees

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Quadrilateral: Four sided polygon.

Types of Quadrilateral:

1)Trapezoid - a quadrilateral with two parallel sides.

2)Rhombus - A quadrilateral with four equal sides and opposite angles equal.

3)Parallelogram - Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other.

4)Rectangle - A parallelogram in which all angles are right angles.

5)Square – It is a special case of a rectangle as it has four right angles and parallel sides. Sum of angles in a Quadrilateral = 360 degrees

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You did great work in learning lesson !

Be sure to practice and keep up the good work