Question

how do you construct congruent segments, segment bisectors, angles, and angle bisectors using tools such as a compass and straightedge?

Explanation:

1. Congruent segments: Use a compass to measure the length of a given segment. Then, with the compass - set width, mark off the same length on another line using a straightedge.
2. Segment bisectors: Place the compass at one end of the segment, open it more than half - the length of the segment. Draw arcs above and below the segment. Repeat from the other end. The line connecting the intersection points of the arcs is the segment bisector.
3. Angles: To construct an angle equal to a given angle, first draw a ray. Place the compass at the vertex of the given angle and draw an arc that intersects both sides of the angle. Measure the distance between the two intersection points on the given angle with the compass. Then, place the compass at the endpoint of the new ray and draw an arc with the same radius. Mark a point on this arc at the measured distance and draw a ray from the endpoint of the new ray through this point.
4. Angle bisectors: Place the compass at the vertex of the angle and draw an arc that intersects both sides of the angle. From each of these intersection points, draw arcs of the same radius inside the angle. The ray from the vertex through the intersection of these two arcs is the angle bisector.

Answer:

To construct congruent segments, use a compass to copy a length. For segment bisectors, use a compass to create arcs from both endpoints and connect the intersection points of the arcs. To construct angles, use a compass to copy the spread of the angle's sides. For angle bisectors, use a compass to create arcs from the angle's sides and connect the vertex to the intersection of inner arcs.