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

Question

Proving Theorems about Lines and Angles
?CD ← → is the perpendicular bisector of AB ¯ ¯ ¯ ¯ ¯ . Point G is the midpoint of AB ¯ ¯ ¯ ¯ ¯ . Points E and F lie on CD ← → . Which pair of line segments must be congruent?
A) AF ¯ ¯ ¯ ¯ ¯ ≅ BF ¯ ¯ ¯ ¯ ¯
B) BG ¯ ¯ ¯ ¯ ¯ ≅ BF ¯ ¯ ¯ ¯ ¯
C) AE ¯ ¯ ¯ ¯ ¯ ≅ AF ¯ ¯ ¯ ¯ ¯
D) BE ¯ ¯ ¯ ¯ ¯ ≅ BF ¯ ¯ ¯ ¯ ¯ 
 

 

Answer 1

Jacinth, 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. 

 

Hope this helps!