This video is provided as supplementary
material for courses taught at Howard Community
College and in this video I’m going to demonstrate three basic
geometric constructions. I’m going to show how to copy a line
segments, how to copy an angle, and how to copy a triangle. So let’s
start with the line segments. I’ve got a line segment here and I want to make a copy of it. The
first step is going to be to draw a line that I’ll make that copy onto. Then, on that line, I’ll place a point that’s
going to be one of the endpoints of my line segment.
The next step is going to be take a compass and set the radius of the compass equal to the length of that line segment. I’ll then place the point of the compass onto the point that I drew on the line and draw an arc through the line. My line segment is going to go from that point to the
place where the arc cut through the line. So I’ve got my original line segment and I’ve got a copy of the line segment.
Let’s go on to copying an angle. I’ve got an angle drawn here and I want to make a copy of it. So the first step is
going to be to draw a ray which is going to be
one of this side of the angle. So I’ll draw a ray, and now I’ll take the compass and I’m going to draw an arc which goes through both sides of my original angle. And I’ll copy that arc onto the ray. I’ll place the point
of the compass at the endpoint of that ray and draw
another arc. And now I’ll, measure using my compass, the distance between the place where
that first arc crossed one side of the angle and the other side. So
I’ll set the compass at that distance, and now I’m going to
copy that distance onto the ray that I’ve drawn
for my second angle. Now all I have to do is connect the end point of the ray with the place where those two arc met. Now I’ve got my original angle and a copy of
that angle. The last construction I want to do is copying
a triangle. So I’ve got a triangle. I’m going to draw a line which is going
to be the base of my new triangle. Since the base of that original triangle is a line segment,
I’m just gonna copy that line segment. So I’ll put one point on this line, for one end of the line
segment, I’ll copy that line segment, which is the base, using my compass. I’ll set the compass equal to that line
segment, equal to the base, and I’ll copy that onto
the line that I’ve drawn here. I want to copy one of the two remaining sides, so I’ll set
the point of the compass onto a vertex, one of the base vertices of my triangle, and set the compass equal to the distance from that vertex to the vertex at the top of the triangle.
And now I’ll copy that distance from the end point of the line segment. And I’ll do the same thing for the other side of the triangle. I’ll
set my compass point at a vertex of the triangle, set the compass equal to that side, and copy that distance onto my new triangle, or what’s going to be my new triangle. And now I’ve just got some points to connect. So I’ve got my original triangle. I copied
the base down here onto the line that I drew. I copied one of the sides onto the triangle, and I copied the third side onto the new triangle. So the three sides are congruent. That means I’ve got two congruent
triangles. That’s all there is to it. Take care. I’ll see you next time.