Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C
Step 2: Open the compass to the length of AB
Step 3: With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.
a. a perpendicular bisector
b. a congruent segment
c. an angle bisector
d. a congruent angle
b. a congruent segment
Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Put the compass point on A and draw a long arc. Be sure the opening is greater than 1/2 AB.
Step 2: With the compass on the same setting, put the compass point on B and draw another long arc. Label the points where the two arcs meet as X and Y.
Step 3: Draw XY. Label the point of intersection of AB and XY as M, the midpoint of AB
a. a perpendicular bisector
The figure that can be constructed using the given steps is:
c. an angle bisector
Using the steps given, we can construct a congruent segment with endpoints C and D.
To construct a congruent segment, follow these steps:
1. Draw a ray with endpoint C.
2. Open the compass to the length of AB.
3. With the same compass setting, put the compass point on point C.
4. Draw an arc that intersects the ray.
5. Label the point of intersection D.
By using the same compass setting, the segment CD will be congruent to the segment AB. Therefore, the correct answer is b. a congruent segment.