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How to Construct Angles Using a Compass & Straight Edge

Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

A compass is a tool used to draw arcs and circles. Even though a compass draws curves, we can use one to draw an angle. In this lesson, we will use a compass and a straight edge to draw a copy of an angle.

Making a Copy

Your teachers use large machines called copy machines to make multiple copies of worksheets or other papers to pass out to the class. What's awesome about copy machines is they make identical copies. We can make identical copies of angles, but we won't use a copy machine. We'll use a compass and an ordinary straight edge. Let's see how to do this!

Copying an Angle

To make a copy of something we need something to make a copy of! Let's draw a random angle that we will make a copy of.


This is the angle we want to make a copy of.
original_angle


Let's start our copy by labeling the vertex of the original angle, A.


The vertex of our angle is A.
A


Now we draw a straight line and put a point on the line, which we'll call point A.


Point A will serve as the vertex point of our copied angle.
aa


Now we get our compass and open it to any angle we want. Put the point of the compass on the A of our original angle and draw an arc through both line segments.


The red arc is what we drew with the compass.
arc


Making sure we don't change the opening of our compass, we put the compass' pointed end on the A of our copy and draw another arc.


Copy of arc from the original angle
arc_copy


Next, we adjust the compass so that it is as wide as points B and C on our original angle drawing.


Adjust the compass so one leg is on point B and the other leg is on point C.
BC


Make sure to keep the compass open to the same angle. Put the pointed end on the intersection of the straight line and the first curve we drew for our copied angle, which is point C. Use the compass to make an arc that will intersect the previous arc.


Drawing an intersecting arc for our copied angle
abc


The last step is to draw a straight line from point A through the intersection of our two arcs, which is point B.


Drawing a line from point A through the intersection of the arcs
final


Now lets put the two angles together to see how we did!


Comparing our original angle with our copied angle
compare


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