3.4 What are
Intersecting Lines?
3.8.1 Parts
of a Coordinate Plane
3.11.1
Family Tree for Quadrilaterals
3.12.1
Congruency of Figures by Transformation
3.13
Sketching Transformations with Coordinate Plane
3.14
Calculating Perimeter Using Grids
By the end of this lesson, you will be able to:
·
Know
about Coordinate plane
·
Sketch
the transformation of figures
·
Solve
the problems related to sum of angles.
Figures that
can lie on a plane surface are known as TwoDimensional figures.
They have
only 2 dimensions, length and width.
Figure 
Image 
Attributes 
Perimeter 

Triangle 
h b 
3 sides 3 vertices 3 angles 
Sum of all the three sides. 

Square 
a a a a 
4 sides 4 vertices 4 angles 
(4 × a) 

Rectangle 
l
b b l 
4 sides 4 vertices 4 angles 
2(l + b) 

Circle 

0 
(2 × π × r) 

Trapezoid 
b
a c 
4 sides 4 vertices 4 angles 
Sum of all the sides. 

Hexagon 
t

6 sides 6 vertices 6 angles 
(6 × t) 
Find the perimeter of the following figures:
1) 2)
7 cm 9 cm
4 cm 4
7 cm 7 cm
9 cm
1) cm
1) The first figure is a square having all the sides equal.
· Side = 7 cm = a
·
Perimeter = 4 × a
·
Thus, Perimeter = 4 × 7 = 28
cm
2) The second figure is a rectangle having length and breadth
· Length = 9 cm = l
· Breadth = 4 cm = b
· Perimeter = 2 ( l + b )
· Thus, Perimeter = 2 ( 9 + 4) = 2 × 13 = 26 cm
Find the perimeter and area of the following figures:
1) 2)
20 ft 25 ft 30 ft
A 4 cm B
10cm 10cm 50 ft
D 18 cm C 45 ft 30 ft
1) The first figure ABCD is a Trapezoid.
· AB = 4 cm ; BC = 10 cm ; CD = 18 cm ; DA = 10 cm.
· Perimeter = sum of all the sides = ( AB + BC + CD + DA )
·
Perimeter = ( 4 + 10 + 18 + 10 ) = 42 cm.
2) Consider the second figure which shows length of different sections of a house.
· Perimeter = sum of all outer boundaries = ( 20 + 25 + 30 + 15 + 35 + 30 + 45 +50 )
· Perimeter = ( 45 + 45 + 65 + 95 ) = 250 ft.
These are like solids. They cannot lie on a plane surface. They have length, width and height. It can be measured in 3 directions. They can be identified by faces, edges and vertexes.
3D gives us depth perception.
· A face is a flat surface.
· An edge is a line formed by 2 faces.
· A vertex is a point where 2 or more edges meet.
The 3D figures which have curved surfaces as below, can be identified by curved surfaces and the flat circular surfaces (bases) on which they rest.
Figure 
Image 
Description 

Square Pyramid 
h s
l l 
·
5 faces ·
8 edges ·
5 vertices 

Cube 
a
a a 
·
6 squre faces ·
12 edges ·
8 vertices 

Cuboid 
h w l 
·
6 faces ·
12 edges ·
8 vertices 

Sphere 
d 
·
1 curved surface. ·
Radius = r = ·
Diameter = d = 2 × r 

Cylinder 
H h
r 
·
1 curved surface. ·
2 circular bases. ·
Radius = r; Heght = h 

Cone 
h l r 
·
1 curved surface ·
1 circular base ·
Height = h; slant height = l; radius = r 
Consider a cuboid as shown below. Find faces, edges and vertices?
A B
F
C
E D
Faces = 6 ( ABGF, GBCD, HCDE, ABHC, FAHE, FGDE )
Edges = 12 (AB, BC, CD, DE, EF, FA, FG, GD, GB, AH, HE, HC )
Vertex = 8 ( A, B , C , D, E, F, G, H )
Identify the given figures and structures:
1) Dice 2) Football
3) Juice Can 4) Duster
The above figure has the following shapes:
Dice 
Cube 
Football 
Spherical 
Juice Can 
Cylindrical 
Duster 
Cuboid 
Lines that are same distance apart at all points are known as Parallel Lines..
Parallel lines will never cross or intersect each other.
Line AB and CD are parallel lines.
B
A
D
C
Identify the parallel lines from the given figures:
1) A B 2) P Q
R S
C D
From the above figures we conclude:
1. In first figure line AB is parallel to line CD and line AC is parallel to line BD.
2. In second figure line PQ is parallel to line RS and line PR is parallel to line QS.
Lines that crosses each other and have one point in common are known as Intersecting lines.
Let the two lines AB and CD intersect each other at P.
C B
P
A D
Perpendicular lines are special type of intersecting line which form right angle where they intersect.
Let us consider two lines PQ and RS which intersect at O.
S
O 90°
P Q
R
Angle O makes 90° and is the common intersecting point of line PQ and RS.
Congruent figures are of same size and shape. When we place one figure over another, they should match exactly.
Shape 
Image 
Same
Shape 
Same
Size 
Rectangles 

Yes 
Yes 
Circles 

Yes 
Yes 
Rectangles 

Yes 
Yes 
Quadrilateral 

Yes 
Yes 
A figure is said to have symmetry if it can be folded to make 2 halves that exactly match each other. The two halves need to be mirror images of each other. We find symmetry everywhere in nature. Fruits, Flowers, Animals, Rainbow, Sun, Moon are some examples.
If we fold ourselves along the line in the middle, the two halves will match exactly
Butterfly is Symmetrical.
Sweet puppy is Symmetrical too. In fact all animals you will find to be symmetrical.









Below are few Symmetrical shapes
There are other figures which are not symmetrical.









The line along which we fold an object to get two equal parts is called Line of Symmetry. Any figure may have one or more Lines of Symmetry.
A figure having at least one Line of Symmetry is Symmetrical.
Consider some of the figures as shown below:
Figures 
No. of Lines of
Symmetry 
Symmetrical 

0 
No 

1 
Yes 

>1 
Yes 
Suppose, you
are standing in a room. Now if someone asks you, what is your location in the
room? What would you say? You would try and estimate your distance from the
door, walls etc and say that, “I am 3 feet from the door” or “I am 3 feet from
the door and 2 feet from the back wall”. This is the origin of the coordinate
system. We define our location at a place by an ordered pair of numbers.
Coordinate
plane is a flat region determined by two perpendicular intersecting number line
called axes. It is sort of a grid which is used to locate points. Each point is
denoted by an ordered pair of numbers. We call each of these numbers the
coordinates. Hence the name, coordinate plane. Here the floor of the room acts
a coordinate plane.
·
Origin:
The starting point so to say. Coordinates are (0,0)
·
X
Axis: The horizontal number line marked ‘x’. Tells us how far right of the
origin a point is.
· Y Axis: The vertical number line marked ‘y’. Tells us how far up from the origin a point is.
4 





3 
(2, 3) 




2 











0 3 



x 
y 5 4 2 1 5 1
Origin (0, 0)
Here we have
located the point (2,3) on the coordinate plane. It is 2 units from x axis and
3 units from y axis. So in the ordered pair, first number is the distance from
x axis and the second number is the distance from y axis. They are named x
coordinate and the y coordinate respectively.
` Find the coordinates of Points A, B, C, D on the coordinate plane.
4 





3 





2 











0 3 



x 
y 5 4 2 1 5 1
Origin (0, 0)
Point 
How far right
to the origin (x coordinate) 
How far up
from the origin (y coordinate) 
Coordinates 
A 
1 
4 
(1, 4) 
B 
0 
3 
(0, 3) 
C 
3 
2 
(3, 2) 
D 
2 
0 
(2, 0) 
Point D Lies on x axis. Its y
coordinate is 0.
Point B Lies on y axis. Its x
coordinate is 0.
Find the coordinates of Pillow
(P), Door (D), Boy (B) on the floor.
With
reference to the given origin (0,0), moving on the x and y axis (direction
shown), find the coordinates of the Pillow P,
Boy B, Door D
Point 
How far left
to the origin (x coordinate) 
How far
forward from the origin (y coordinate) 
Coordinates 
P 
5 
0 
(5, 0) 
B 
2 
2 
(2, 2) 
D 
0 
1 
(0, 1) 
Notice that x is not to
the right of origin but to the left here
Notice that y is below
the origin but forward.
Here we just need to
follow the direction of the arrow (x and y).
Two Dimensional closed figures with straight sides are called Polygons. Circle is a closed figure but is not a polygon.
Various types of
Polygons:
Name 
Image 
Number of Sides 
Number of Angles 
Triangle 

3 
3 
Quadrilateral 

4 
4 
Pentagon 

5 
5 
Hexagon 

6 
6 
Triangle is
a polygon having 3 sides and 3 angles. Sum of the angles is 180°.
Types of Triangles on
the basis of sides

Equilateral Triangle 
All 3 sides are equal All three angles are 60° 

Isosceles Triangle 
Two sides are equal Two angles are equal 

Scalene
Triangle 
No sides are equal No angles are equal 
Types of Triangles on
the basis of angles

Right Triangle 
One 90° angle 

Acute Triangle 
All angles < 90° 

Obtuse
Triangle 
One angle > 90° 
Any two
dimensional shape with four straight sides is a quadrilateral
(Quad means
four; lateral means side, hence quadrilateral)
·
Four
Sides
·
Four
Vertices
·
Sum
of interior angles equals 360 degrees.
Figure 
Image 
Attributes 



Square 
a
a a
a 
4 equal sides. Opposite sides are
parallel 
4 equal right angles (90°) 


Rectangle 
l
b b
l 
Opposite sides are equal and parallel 
4 equal right angles (90°) 
Square is a rectangles with all sides equal 

Parallelogram 

Opposite sides are
equal and parallel 
Opposite angles are
equal 


Rhombus 

4 equal sides Opposite sides are parallel 
Opposite angles are equal 
Diagonals intersect at 90° Rhombus is a parallelogram with all
sides equal. 

Trapezoid/ Trapezium 
b
a c 
One pair of opposite sides is equal 



Kite 

Two pair of adjacent equal sides 
Angles where pairs meet are equal 
Diagonals intersect at 90° 
· Changing the position of a shape by rotation, reflection or translation is known as transformation.
· Size, area and length of the shape are unaltered.
· Turn, flip and slide are some of the basic moves.
· We can verify congruency of figure through these transformations.
Consider an example as shown below:
Rotation B
A
( Turn)
C

A’
B’
Turn C’ 

B Reflection
A
( Flip )
C 
B’ A’ C’ Flip 

A C Translation ( Slide)
B 
A’ C’
Slide B’ 
If we only
rotate, reflect or translate the shape then the two shapes are congruent
If we need
to resize it then two shapes are similar
Rotate 
Congruent 
Reflect 

Translate 
· The size of the figure remains the same after turn, flip or slide.
· Two shapes of same size are said to be congruent when they can be superimposed on one another.
· All congruent triangles are similar but all similar triangles are not congruent.
· Size can be different for similar triangles or species.
· Size should be exact same for congruency.
Reflection (Flip)
·
Measure
the distance of all the vertex points from the y axis.
·
Mark
the same distance on the other side of the y axis
·
Join
up the dots








































































































































































































Translation (Slide)
·
Move
all the vertexes to equal distance, along the x axis (here 8 places)
·
Join
up the dots








































































































































































































Rotation (Turn)
We are doing
here translation followed by rotation.
·
Rotate
the two adjacent lines by the same angle
·
Join up the points













