Parallel and Perpendicular Lines
This lesson explains what are parallel and perpendicular lines and has varied exercises for the students. The lesson also includes a video where I show how to draw a perpendicular line and a rectangle using a protractor or a triangular ruler.
Two lines or line segments can either intersect (cross) each other or be
parallel. Think of the parallel lines as never meeting each other, no matter how much you would continue them to both directions. 
These lines intersect. 
These lines are parallel. 
We say two lines or line segments are perpendicular if they form a right angle (or several right angles). We can mark a right angle with a little corner . 
How many right angles 
The line segments AB 
1. What about these lines? Do they intersect or are they
parallel? Continue the lines with your ruler.
2. Which line segments in these figures are parallel? Which are perpendicular?



How to draw a right angle (perpendicular line) and a rectangle
In the video below, I show you how to a right angle (or a perpendicular line to a given line) using either a protractor or a triangular ruler. I also show how to draw a line perpendicular to a given line through a point on the line, or through a point not on the line. Lastly, I draw a rectangle with given side lengths, using a protractor to make right angles, and a regular ruler to measure the sides.
How to draw a line that is perpendicular to a given line  


1) Using a protractor:
Align the dot and the straight side of your protractor.

Draw the line. 

2) Using a triangular ruler:
Align the inside edge with the given line. 
Draw the line. 
3. Draw perpendicular lines through these points.
4. Draw a line that is perpendicular to the given line and goes through the given point.
5. Complete these drawings so you get: a) a rectangle;
b) a square. Use a protractor or a triangular
ruler to make sure the lines you draw are perpendicular to
the existing lines.
a.  b. 
6. a. Draw here any triangle that has a right
angle. It is called a right triangle.
(Hint: Start by drawing two lines that are perpendicular.)
b. Find the perimeter of your triangle in centimeters/millimeters.
Draw a line that is parallel to a given line. Method 1: A ruler. 
Align the
bottom side of the ruler with an existing
line.
You can carefully slide the ruler up or down
if you need 
Method 2: A protractor. 




7. Sketch many lines that are parallel to this line. Use method 1. Then draw one line that is perpendicular to them all! 

9. Draw a square with 5 cm sides.
Hint: first draw a line, longer than 5 cm.
Mark two points on it, 5 cm apart. Now
draw two lines perpendicular to your
starting line that go through those points.
10.
Find rays, lines, and line segments that are either parallel or perpendicular to
each other. You can use
these shorthand notations: ∥ for parallel and ⊥
for perpendicular.
For example, l ∥ m means l is parallel to m, and
AB ⊥
CD means
AB is perpendicular to
CD.
b. 
This lesson is taken from Maria Miller's book Math Mammoth Geometry 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Geometry 1
A selfteaching worktext for 4th5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!
Download ($6.90). Also available as a printed copy.