Given: C is the midpoint of line segment AE. C is the midpoint of line segment BD. AE is congruent to BD. Prove: AC is congruent to CD

Answer 1

Draw a figure.

The hypotheses of the problem make all 4 segments which intersect at C equal to each other!!!!!

Answer 2

AE = BD given

AC + CD = AE; BC + CD = BD segment addition postulate

AC + CE = BC + CD substitution

AC = CE; BC = CD definition of midpoint

AC + AC = CD + CD substitution

AC = CD subtraction