Copying an angle with compass and straightedge

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Copying an Angle

Click here for a printable angle copying worksheet

This demonstration shows how to make a copy of an angle using only a compass and straight edge. See "Introduction to Euclidean Constructions" We start with an angle ∠BAC. The result is another angle ∠QPR congruent to the first.

Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.

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Note that the straightedge can be a ruler, but it is not used to actually measure anything, just to draw straight lines. Ignore the markings on it.

Step-by-step Instructions

Step 1	Using the straightedge, draw a reference line and place a point P near the left end.
Step 2	Set the compass width to the distance AC, and without adjusting the compass, place it on P and mark an arc across the line. This establishes the point Q
Step 3	With the compass on point A set its width to the the point B.
Step 4	Without changing the compass width, place the compass point on the the point P and draw an arc above the line.
Step 5	Place the compass point on C and set its width to the point B.
Step 6	Without changing the compass width, place the compass point on the the point Q and draw an arc across the previously drawn arc. The intersection of these two arcs becomes point R.
Step 7	Using the straightedge, draw a line from point P to R where the arcs intersect.
Step 8	Done. The angle ∠QPR is congruent (equal in measure) to angle ∠CAB.

Try it yourself

Click here for a printable worksheet containing twoangle copying problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions