A congruent angle is created when an exact replica or copy is made. Since the angle sides do not have lengths (they are rays that extend without end from a point called the vertex), the only measurement that needs to match is the angle measurement. Directions for constructing a congruent angle to an original are described below, step by step. Try using your compass and straightedge to construct the angle as you follow along with the directions. You can use a protractor when you are finished to check your work, but remember not to use one in your construction.
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Start by drawing angle BAC.
Make a point P that will be the vertex of the new angle.
From P, draw a ray PQ. This will become one side of the new angle. This ray can go off in any direction. It does not have to be parallel to anything else.
Place the compass tip on point A, set to any convenient width.
Draw an arc across both sides of the angle, creating the points J and K as shown.
Without changing the compass's width, place the compass point on P and draw a similar arc there, creating point M as shown.
Set the compass on K and adjust its width to point J.
Without changing the compass's width, move the compass to M and draw an arc across the first one, creating point L where they cross.
Draw a ray PR from P through L and onwards a little further. The exact length is not important.
The angle ∠RPQ is congruent (equal in measure) to angle ∠BAC. |
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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.
