Amy has a master's degree in secondary education and has taught math at a public charter high school.
In this video lesson, you will see how to use geometric construction to draw perpendicular lines. Learn why geometric construction is useful. Also find out the only two tools in addition to your pencil that you need to do this.
Let's begin by talking about perpendicular lines. What exactly are they? Perpendicular lines can be defined as lines that intersect each other at 90 degree angles. Where do you see these in real life? Power poles are usually built perpendicular to the ground if the ground is flat and not on a hill. Also the window screens that keep bugs out are made with perpendicular lines. Take a close look at them and you will see tiny little squares and lots of perpendicular lines intersecting each other.
Why would you want to draw perpendicular lines? If you were an architect or an artist and you wanted to draw perpendicular lines to accurately portray something but you didn't have a way to measure angles, you would use geometric construction to draw your lines.
Geometric construction is the drawing of lines, shapes, and angles with only a pencil, compass, and straight edge. There are no numbers or any measuring involved at all. This is the method that you will learn in this video lesson. So if you have your own compass and straight edge, go ahead and grab them so you can follow along.
Setting It Up
To start, we are going to draw a line. Somewhere above the line we are going to draw a dot C. This point C is the point through which we are going to draw our perpendicular line.
Now take your compass and set one point on point C. Set the width of the compass so that the other end extends past your line. Now draw two arcs that intersect the line to the left and right of the point C. Label the intersection to the left point A and label the intersection to the right point B. You now have a line segment AB.
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Next, without changing the width of the compass, move one end of the compass to point A and draw an arc underneath the line segment below the point C. Move the compass to point B and do the same. You should have two little arcs underneath your line segment that intersect each other. Label this intersection point D.
To finish, take your straight edge and connect points C and D. You can draw the line as long or as short as you like.
One interesting thing about this process is that the perpendicular line that results from this process also bisects the line segment you created. Yes, your line segment AB is split exactly in half by the perpendicular line segment CD.
What have we learned? We've learned that a perpendicular line is a line that intersects another line at 90 degree angles. If we didn't have a way to measure anything, we would use geometric construction to create perpendicular lines.
Geometric construction is the drawing of lines, angles, and shapes with only a pencil, compass, and straight edge. No measuring or numbers are involved. To draw our perpendicular lines, we start with a line and a point not on the line. We then create a line segment that we use to help us construct our perpendicular line.
After completion of this lesson, you should be able to explain and model what perpendicular lines are and how to construct them.
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