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Constructions

This guide covers fundamental construction techniques in geometry. Learn how to bisect a segment by drawing arcs from points A and B to find the midpoint M. Discover how to construct the angle bisector by placing a compass at point C, creating arcs that intersect the angle’s sides, and drawing a ray through the intersection. Lastly, master the method to draw a line through a point not on a given line using compass and straightedge techniques. Perfect for students and anyone looking to strengthen their geometry skills.

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Constructions

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  1. Constructions

  2. A B Construction #1: Construct the Bisector of a Segment • Place the compass point at A. Draw an arc using a • compass setting greater than half the length of • 2. Place the compass point at B. Draw an arc. It should • intersect the other arc at two places. • 3. Use a straightedge to draw a segment through the • points of intersection. This segment bisects at • M, the midpoint of .

  3. C Construction #2: Construct the Angle Bisector • Place the compass point at C. Draw an arc that intersects • both sides of the angle. Label the intersections A and B. • 2. Place the compass point at A. Draw an arc. Then place the • point at C. Using the same compass setting, draw another • arc. • 3. Label the intersection D. Use a straightedge to draw a ray • through C and D. This is the angle bisector.

  4. P A B Construction # 3: Construct a to a line through a point not on the line. • Place the compass at “P”. Draw an arc that intersects line “m” twice. Label the intersections as A and B. • Open your compass a little. Draw an arc around A. With the same setting, draw an arc around B. Label the intersection “C”. • Use ruler to draw line CP.

  5. Assignment Constructions Worksheet

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