Directions for constructing a 45 ° angle are described below, step by step. Try using your compass and straightedge to construct the angle as you follow along with the directions.
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Draw a line segment of any length, PQ. P will be the angle's vertex.
Set the compass's width to just over half the length of the line segment PQ.
With the compass's point on P then Q, draw two arcs that cross above and below the line.
Draw a line between the two arc intersections. This forms a perpendicular bisector of segment PQ. This means that segment PQ is divided in half and there are four right angles formed.
With the compass's point on the intersection of segment PQ and the perpendicular just drawn, set the compass's width to P.
Draw an arc across the perpendicular, creating the point C.
Draw a line from P through C, and on a little more. Label point R on this line.
Done. The angle ∠QPR has a measure of 45°. |
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To see an animation of the construction, click the play button below. This animation does not include audio - it only shows each step as it occurs in the correct order.
Question
What do steps 2, 3, and 4 create in the process of creating a 45 degree angle?
