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.