Question

Given the following:

CD←→ is the perpendicular bisector of AB¯¯¯¯¯
Point G is the midpoint of AB¯¯¯¯¯
Points E and F lie on CD←→
Identy the pair of line segments that must be congruent.

Answer 1

The answer is A

Answer 2

I encountered this question before, it had choices. They were the following:
A) AF ¯ ¯ ¯ ¯ ¯ ≅ BF ¯ ¯ ¯ ¯ ¯
B) BG ¯ ¯ ¯ ¯ ¯ ≅ BF ¯ ¯ ¯ ¯ ¯
C) AE ¯ ¯ ¯ ¯ ¯ ≅ AF ¯ ¯ ¯ ¯ ¯
D) BE ¯ ¯ ¯ ¯ ¯ ≅ BF ¯ ¯ ¯ ¯ ¯

Remember that any point on your perpendicular bisector is the same distance from the points on either end of your bisected line segment. This means that point E should be the same distance to A as it is to B, and point F should also be the same distance from A as it is to B. This means that A is our answer.