Question

Isaac will be constructing congruent segments with a compass and straightedge, while Micah will be constructing a segment bisector with a compass and straightedge. Describe the similarities and differences between their construction steps.

Answer 1

What do you think?

Answer 2

In order to find the answer to this question you must explain the steps of constructing congruent segments, and explain the steps of constructing a segment bisector with a compass and a straightedge then list all the similarities and differences after you do so.

Steps to constructing a congruent segment with a straightedge and compass:

1. Draw the points of intersection between each arc and the ray, or rays, it intersects.
2. Open the compass to the width of the intersection points between the arc and the two rays.
3. Use a straightedge to create a ray.
4. Place the tip of your compass on the vertex of the given angle, and swing an arc that intersects both rays of the given angle.
5. Use the compass to draw an arc from the endpoint.
6. Draw a point where the two arcs intersect.
7. Keeping the compass width the same, draw an arc from the point of intersection.
8. Use your straightedge to draw a ray between endpoint, and the point of intersection.


Steps to constructing a segment bisector with a compass and a straightedge:

1. Place the compass at one end of line segment.
2. Adjust the compass to slightly longer than half the line segment length
3. Draw arcs above and below the line.
4. Keeping the same compass width, draw arcs from other end of line.
5. Place ruler where the arcs cross, and draw the line segment.


One difference between two steps is that while one draws points between arcs the second set of steps only requires you to place the compass at one end of the segment. Both set of steps require you to keep the same width throughout the process of construction. Both steps require you to draw arcs using the compass. One set of steps requires you to draw a point from where the lines intersect while the other doesn't. One set of steps require you to swing a arc while the other set of steps does not.

Hope this helps.