Wendy drew line segment LM. She used a compass and straightedge and constructed a bisector on segment LM that crosses it at O.

Which other construction uses the same steps as the ones Wendy took?
A:an angle bisector
B:a congruent angle
C:a pair of parallel lines
D:a pair of perpendicular lines

To determine which other construction uses the same steps as the ones Wendy took to construct the bisector on segment LM, let's examine each option:

A: An angle bisector: To construct an angle bisector, we use a compass and straightedge just like Wendy used. We draw arcs from the vertex of the given angle, then connect the intersections of those arcs with the angle's sides to find the bisector. This construction is similar to what Wendy did, so option A is a possible answer.

B: A congruent angle: To construct a congruent angle, we need to use a compass and straightedge to ensure both angles have the same measure. In this case, Wendy did not construct an angle but a line segment bisector, so option B is not a correct answer.

C: A pair of parallel lines: Constructing a pair of parallel lines requires a different approach than what Wendy used. We would need to use a compass and straightedge to draw a transversal line that intersects two given lines at distinct points, then construct the parallel lines using various geometric properties. Thus, option C is not a correct answer.

D: A pair of perpendicular lines: Similarly to option C, constructing a pair of perpendicular lines would involve a different set of steps. We would need to use a compass and straightedge to draw right angles at the given points of intersection. Therefore, option D is not a correct answer.

In conclusion, the other construction that uses the same steps as the one Wendy took is option A: an angle bisector.