Select the choice that indicates ⟷PQ is the perpendicular bisector of ⟷XY if they intersect at M

Question

• PM ≅ QM
• XY ⊥ PQ and XM ≅ YM
• PQ ⊥ MY
• PQ ⊥ MY and PM ≅ QM

Answer 1

The choice that correctly indicates that ⟷PQ is the perpendicular bisector of ⟷XY if they intersect at M is:

• XY ⊥ PQ and XM ≅ YM

This choice denotes that line segment XY is perpendicular to PQ, and that M is the midpoint of XY, which means XM is congruent to YM. Both of these conditions must hold for PQ to be the perpendicular bisector of XY.