Question

In square ABCD, F and G are the midpoints of segments CD and AB, respectively. Which statement is true?


Answer BF = 2CF
DG = 2AG
BF = DG
BF = DG = BC

Answer 1

Automatically, what is first noticed is that the two lines form 2 triangles in opposite corners of the square formed at midpoints F and G. Well since F is the midpoint of CD, you can determine that the segments CF and DF are congruent since it is bisecting it. This is similar to the segment opposite it ( line AB). And since it is a square, the corners within it are all 90 degree angles providing further evidence to these triangles being congruent do to the theorem of same side, angle, and side (SAS), meaning that all sides within the triangles are also congruent. Now referring back to the previous statements made, the conclusion that is to be made is that line segments BF and DG are congruent

Answer 2

Just use pythagoras. BF=DG but not BC