Construction

Copying an Angle Using a String

Using a straightedge and a string, it is possible to construct a copy of an angle.

The following five steps can be used to draw an angle whose measure is equal to the measure of ∠ ABC.

Draw a Ray with Starting Point E

To begin, draw a ray using a straightedge and label its starting point as E.

Draw Arcs Centered at B and E Using the String

Start by tying a pencil to one end of the string and locating the other end at B. The string must be shorter than the sides of the angle.

Next, holding down the end that is on B, stretch the string. Keeping the string stretched, make an arc that intersects the sides of ∠ ABC. Let P and Q be these points of intersection.

Finally, move the free end of the string to E and draw an arc centered at E. Let D be the intersection point between the ray and the arc.

Measure the Distance from P to Q

To measure the distance between P and Q, untie the pencil. Then, place one end of the string at P and hold it down. Next, stretch the string so that it forms a straight line that passes through Q.

Then, mark the point on the string that is on Q and tie the pencil to the string so that its tip is over the mark. It is not a necessity, but the remaining part of the string can be removed.

Draw an Arc Centered on D with Radius PQ

Move the free end of the string to D and make an arc that intersects the previous arc. Let F be the intersection point.

Draw EF

Using the straightedge, draw EF. This ray along with ED form ∠ DEF whose measure is equal to the measure of ∠ ABC.

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