Question

CD is the perpendicular bisector AB. G is the midpoint of AB. points E and F lie on CD. which pair of line segments must be congruent?

Answer 1

AE and BE

Explanation:

Please refer to the image attached with this.

Here in we have made a diagram a per the conditions given in the question. If we observe ΔABE, We see

AG=GE ( CD is perpendicular bisector of AB , Hence G is mid point)

∠AGE = ∠BGE = 90°

GE = GE

Hence

ΔAGE ≅ ΔBGE

Therefore the theorem of congruent triangles ,

AE ≅ BE