CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Perpendicular, parallel & intersecting

linesLet’s warm up :

1) Name a line segment with R as an end point.

2) Name a ray with R as an end point.

3) Name a ray with S as an end point.

4) Name two line segments with S as an end point.

RQ

S T

1) SR

2) RQ

3) ST

4) SR, ST

CONFIDENTIAL 2

Let’s review what we did in the last session

Geometry is all about shapes and their properties.

The two most common subjects in geometry are:

1) Plane Geometry

2) Solid Geometry

Plane geometry: is the study of plane figures in the plane such as points, lines, line segments,

rays, angles, circles, triangles, quadrilaterals, and other polygons ... shapes that can be drawn on a

piece of paper.

Solid Geometry: is the study of three dimensional objects like cubes and pyramids. It

is called three-dimensional, or 3D because there are three dimensions: width, depth and

height.

CONFIDENTIAL 3

Review

Point

A point is an exact location .

Points are dimensionless,i.e., a point has no width, length, or height.

We locate points relative to some arbitrary standard point, often called the "origin".

A point is a location in space.

X

CONFIDENTIAL 4

Review

A line is a group of points on a straight path that extends to infinity.

Any two points on the line can be used to name it. This line is called line DE.

Its length, having no limit, is infinite.

It has no width or height.

D E

DE

Line

CONFIDENTIAL 5

Review

A line segment is a part of a line that has two end points.

A line segment is the path of shortest distance between two points.

The two end points of the line segment are used to name the line segment. This line segment is called

segment XY.

All the points "between" the two points make up a line segment.

A line segment has one dimension, length. It has no width or height.

XYX Y

Line segment

CONFIDENTIAL 6

Review

A ray is part of a line. A ray extends indefinitely in one direction, but ends at a single point in the

other direction. That point is called the end-point of the ray.

Ray

A ray is named starting with its end point first and then any other point on the ray second.

O POP

This ray is called ray OP.

CONFIDENTIAL 7

A line has no end-points.

NOTE:

A line segment has two end-points. A ray one end-point.

A

D

B

C

O

Using the graphic in the figure we see that:

A, B, C, D and O are points.DB is a line.AC, OC, and AC are line segments.OD and OB are rays.

Review

CONFIDENTIAL 8

Review

6

5

4

3

2

1

1 2 3 4 5 6

X- scale

Y- scale

Draw a line segment between points (1,5) and (5,5) on the XY-scale.

STEP1:

Mark the points (1,5) and (5,5) on the XY-scale.

X X

point (1,5)

point (5,5)

CONFIDENTIAL 9

Review

STEP2:

Join the points (1,5) and (5,5) on the XY-scale..

6

5

4

3

2

1

1 2 3 4 5 6

X X

Y- scale

X- scale

CONFIDENTIAL 10

Let’s start withPerpendicular, parallel & intersecting lines

For any two lines in the same plane, one of two relationships can occur:

The lines will run parallel to each other,

They will intersect.

OR

CONFIDENTIAL 11

Parallel lines

Lines are parallel if they are always the same distance apart (called "equidistant"), and will

never meet.

They will travel to infinity in either direction and never intersect.

Lines m and l are parallel lines.

l

m

CONFIDENTIAL 12

Intersecting lines

Lines can only intersect at one point and only one point.

x

y

Two or more lines that meet at a point are called intersecting lines. That point would

be on each of these lines.

In the Figure, lines x and y are intersecting lines and intersect at point Q.

Q

CONFIDENTIAL 13

s

t

If the line segments meet or cross each other to form square corners, they are perpendicular to

each other.

Perpendicular lines.

The little box drawn in the corner, means "at right angles“.

right angles

CONFIDENTIAL 14

In other words,when two lines intersect and form right angles (90°), they

are called perpendicular lines. Lines s and t are perpendicular lines.

Perpendicular lines.

Perpendicular lines intersect at a point and form 4 right angles.

s

t

Perpendicular lines form 4

square corners.

CONFIDENTIAL 15

What is the difference between perpendicular and parallel?

90 degrees (a right angle) If you rotate a perpendicular line by 90° it will become

parallel (but not if it touches!), and the other way around.

perpendicular lines

rotate parallel

CONFIDENTIAL 16

Symbol

Meaning Example In Words

|| parallelEF||GH

The line EF is parallel to line GH

perpendicular AB CD

The line AB is perpendicular to line

CD

Right angle

is 90°

A right angle is 90 degrees

Symbols in Geometry

Here are the some geometrical symbols:

CONFIDENTIAL 17

BREAK

CONFIDENTIAL 18

GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/11-16-06-merry.html

CONFIDENTIAL 19

Assignments

Classify each pair of lines as parallel, intersecting, or perpendicular.

4

1 2

3

1) Parallel2) Intersecting

3) Perpendicular4) Parallel

CONFIDENTIAL 20

Classify each pair of lines as parallel, intersecting, or perpendicular.

8

5 6

7

5) Perpendicular

8) Perpendicular

7) Parallel

6) Intersecting

CONFIDENTIAL 21

Very Good!Let's Review

For any two lines in the same plane, one of two relationships can occur:

The lines will run parallel to each other,

They will intersect.

OR

CONFIDENTIAL 22

Review

Parallel lines

Lines are parallel if they are always the same distance apart (called "equidistant"), and will

never meet.

They will travel to infinity in either direction and never intersect.

Lines m and l are parallel lines.

l

m

CONFIDENTIAL 23

Review

Intersecting lines

Lines can only intersect at one point and only one point.

x

y

Two or more lines that meet at a point are called intersecting lines. That point would

be on each of these lines.

In the Figure, lines x and y are intersecting lines and intersect at point Q.

Q

CONFIDENTIAL 24

Review

s

t

If the line segments meet or cross each other to form square corners, they are perpendicular to

each other.

Perpendicular lines.

The little box drawn in the corner, means "at right angles“.

right angles

Perpendicular lines intersect at a point and form 4 right angles.

CONFIDENTIAL 25

Review

What is the difference between perpendicular and parallel?

90 degrees (a right angle) If you rotate a perpendicular line by 90° it will become

parallel (but not if it touches!), and the other way around.

perpendicular lines

rotate parallel

CONFIDENTIAL 26

Review

Symbol

Meaning Example In Words

|| parallelEF||GH

The line EF is parallel to line GH

perpendicular AB CD

The line AB is perpendicular to line

CD

Right angle

is 90°

A right angle is 90 degrees

Symbols in Geometry

Here are the some geometrical symbols:

CONFIDENTIAL 27

You have done a nice job.See you in the next session.