Question

question 4 2 pts when constructing the perpendicular bisector, which of these statements explains possible reasons the bisector is perpendicular? the intersection points are reflections over the segment, and reflections are perpendicular to the line of reflection. the points of reflection create an isosceles triangle with the segment which can be bisected. the construction creates a rhombus which has perpendicular diagonals. all listed choices.

Explanation:

• When constructing a perpendicular bisector:
• For the first option: In geometric construction, when we create the arcs (intersection points) for a perpendicular bisector, these points are reflections over the segment. By the property of reflections, the line joining the reflection points (the bisector) is perpendicular to the line of reflection (the original segment).
• For the second option: The two intersection points (from the arc - based construction) and the endpoints of the segment form two isosceles triangles. The line that bisects the segment (the perpendicular bisector) also bisects the vertex angle of these isosceles triangles, and in an isosceles triangle, the median (which is the perpendicular bisector in this case) is perpendicular to the base (the original segment).
• For the third option: The four - point figure (formed by the two intersection points and the two endpoints of the segment) is a rhombus (all sides are equal as they are radii of the same - sized arcs). In a rhombus, the diagonals are perpendicular to each other. One diagonal is the original segment and the other is the perpendicular bisector.

Answer:

All listed choices.