Upload
ralph-bridges
View
221
Download
0
Embed Size (px)
Citation preview
Confidential 1
Confidential 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 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
Confidential 6
Classifying Triangles according to the Length of their Sides
Scalene Triangles
Equilateral Triangles
Isosceles Triangles
Confidential 7
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
Confidential 8
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.
Confidential 9
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
Confidential 10
Classifying Triangles according to the Length of their Angles
Acute-angled Triangles
Obtuse-angled Triangles
Right-angled Triangles
Confidential 11
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
Confidential 12
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
Confidential 13
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
Confidential 14
ExampleExampleName the following triangles:
2)
1) Isosceles
triangle
Draw a square around the right triangle:
Confidential 15
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
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
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.
Confidential 19
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.
Confidential 20
RECTANGLERECTANGLE
Opposite sides of a rectangle are parallel and equal in length.
All angles are equal to 90°.
A B
CD
Confidential 21
SQUARESQUARE Opposite sides of a square are parallel and all
sides are equal in length.
All angles are equal to 90°.
A B
CD
Confidential 22
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
Confidential 23
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)
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
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 + 128 = 180x + 128 - 128 = 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
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
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) 10 + 20 = 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 TriangleSum 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