Construct a 90° angle, and then construct an angle bisector to obtain a 45° angle.
Step 1: Stretch your compasses until it is more then half the length of AB. Put the sharp end at A and mark an arc above and another arc below line segment AB.
Step 2: Without changing the width of the compasses, put the sharp end at B and mark arcs above and below the line segment AB that will intersect with the arcs drawn in step 1.
Step 2: Without changing the width of the compasses, put the sharp end at B and mark arcs above and below the line segment AB that will intersect with the arcs drawn in step 1.
Join the two points where the arcs intersect with a straight line. This line is the perpendicular bisector of AB. P is the midpoint of AB.
Step 4: Bisect the 90-degree angle to form a 45-degree angle.
In summary the steps to construct a 45° angle are:
Construct perpendicular lines to obtain a 90° angle.
Bisect the 90° angle to obtain a 45° angle.
How to construct a 45-degree angle using compass and straightedge?
Step 1: Construct perpendicular lines (90 degrees).
Step 2: Bisect that angle to get a 45-degree angle.
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