1. Basic Constructions

2. Constructing Segments and Angles
A straightedge and a compass are used to draw geometric figures in construction. A straightedge is a ruler with no markings on it. A compass is a geometric tool used to draw circles and parts of circles called arcs.

3. Constructing Segments and Angles
Four basic constructions involve constructing congruent segments, congruent angles, and bisectors of segments and angles.

4. Constructing Congruent Segments
Given a segment:
Draw a ray.
Open the compass to the length of the given segment.
With the same compass setting, put the compass point on the endpoint of the ray. Draw an arc that intersects the ray.

5. Constructing Congruent Segments

6. Constructing Congruent Angles
Given an angle:
Draw a ray.
With the compass point on the vertex of the given angle, draw an arc that intersects the sides of the given angle. Label the points of intersection.

7. Constructing Congruent Angles
3. With the same compass setting, put the compass point at the endpoint of the ray. Draw an arc and label the point of intersection. 4. Open the compass to the length of the result in #2. Keeping the same setting, put the compass on the result of #3. Draw an arc and locate the point of intersection

8. Constructing Congruent Angles
5. Draw a ray using the endpoint of ray in #1 and the point, which is the result of #4.

9. Constructing Congruent Angles

10. Constructing Bisectors
Perpendicular lines are two lines that intersect to form right angles. The symbol means “is perpendicular to.” A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment into two congruent segments.

11. Constructing the Perpendicular Bisector
Given a segment:
Put the compass point on one endpoint of the segment, draw a long arc. Be sure that the arc opening is more than half of the segment.
With the same compass setting, put the compass point at the other endpoint of the segment. Draw another long arc. Mark the two points where the two arcs intersect

12. Constructing the Perpendicular Bisector
3. Draw a line connecting the two points of intersection. This resulting line is the perpendicular bisector of the given segment. 4. The point of intersection of the given segment and the result of #3 is the midpoint of the given line.

13. Constructing the Perpendicular Bisector

14. Constructing the Angle Bisector
An angle bisector is a ray that divides an angle into two congruent coplanar angles. Its endpoint is at the angle vertex. Within a ray, a segment with the same endpoint is also an angle bisector. It may be said that the ray or segment bisects the angle.

15. Constructing the Angle Bisector
Given an angle:
Put the compass on the vertex of the given angle. Draw an arc that intersects the sides of the angle. Label the points of intersection.
Put the compass on one of the points of intersection (result of #1) and draw an arc. With the same compass setting, draw an arc using the other point (result of #1).

16. Constructing the Angle Bisector
Be sure the arcs intersect. Label the point where the two arcs intersect. 3. Connect the vertex of the given angle and the result of #2.

17. Constructing the Angle Bisector