Confidential 1

2 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.

Confidential 3 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

Confidential 4 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

Confidential 5 Lets get started Triangle:- 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 d side 3 Angle A + Angle B + Angle C = 180 degrees

Confidential 6 Classifying Triangles according to the Length of their Sides Scalene Triangles Equilateral Triangles Isosceles Triangles

Confidential 7 Scalene Triangles Scalene 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. a b c x y zD E F

Confidential 8 Equilateral Triangles Equilateral Triangles An equilateral triangle has all three sides equal in length. Its three angles are also equal and they are each 60 degrees.

Confidential 9 Isosceles Triangles Isosceles Triangles An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal. a a x x

Confidential 10 Classifying Triangles according to the Length of their Angles Acute-angled Triangles Obtuse-angled Triangles Right-angled Triangles

Confidential 11 Acute-angled Triangle 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

Confidential 12 Obtuse-angled Triangle 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. a Longest side

Confidential 13 Right-angled Triangle 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 hypotenuse

Confidential 14 Example Name the following triangles: 2) 1) Isosceles triangle Draw a square around the right triangle:

Confidential 15 Your turn Identify the following types of triangles: 1) ___- a triangle with no equal sides. Scalene triangle 2) ____- a triangle with a right angle. Right Triangle 3) _____- a triangle with at least two sides equal. Isosceles triangle 4) _____- a triangle with three acute angles. Acute Triangle 5) ____- a triangle with three equal sides. Equilateral Triangle

Confidential 16 Quadrilateral A four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees. The figure represents the types of quadrilaterals.

Confidential 17 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

Confidential 18 PARALLELOGRAM  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 C D B ▪ ▪ ● ● Note: Rectangles and squares are special kinds of parallelograms.

Confidential 19 RHOMBUS  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 C Note: A parallelogram with four equal sides is called a rhombus.

Confidential 20 RECTANGLE  Opposite sides of a rectangle are parallel and equal in length.  All angles are equal to 90°. AB C D

Confidential 21 SQUARE  Opposite sides of a square are parallel and all sides are equal in length.  All angles are equal to 90°. A B C D

Confidential 22 Example 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 ) In ________ trapezoid, base angles are equal. Regular 5) Name the quadrilateral whose angles are 90 degree. Square

Confidential 23 Your 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 of Parallelograms. True 3. A quadrilateral with only 1 pair of parallel sides is called ________. Trapezoid 4. What is a parallelogram with 4 right angles and 2 pairs of equal sides. Rectangle 5. Example of quadrilateral is ______. Rhombus (Rhombus, triangle)

Confidential 24 BREAK TIME!!!!

Confidential 25 LETS PLAY A GAME Click Here to Play

Confidential 26 Calculate the size of the missing angle in the following triangle. 80  48 

Confidential 27 Find the angle x in the given diagram. A B C D 68  126  106  xx

Confidential 28 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.

Confidential 29 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

Confidential 30 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.

Confidential 31 Sum of angles in a triangle = 180 degrees Sum of angles in a Quadrilateral = 360 degrees

Confidential 32 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  = 180  x   = 180  -128  x = 52  So, the missing angle is 52 

Confidential 33 Find the angle x in the given diagram. A B C D 68  126  106  xx Solution: x = 360 (Angle of a quadrilateral =360) x = 360 (Subtract 300 from both sides) x – 300 = 360 – 300 x = 60

Confidential 34 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) = 5x – 2x 30 = 3x divide by 3 on both sides x = 10 4x – 1 => 4(10) -1 = 40 – 1 = 39

Confidential 35 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 Sum of angles in a triangle = 180 degrees

Confidential 36 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

Confidential 37 You did great work in learning lesson ! Be sure to practice and keep up the good work