Question 1148913
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 A------B----------C----------D------E

C is the midpoint of BD and AE, prove AB is congruent to DE

Since C divides BD and AE, each into two equal halves, we can say
|BC| = |CD|   
and   
|AC| = |CE|   


Now, starting with |AC| = |CE|, we re-write in terms of the shorter segments: 
|AB| + |BC| = |CD| + |DE| 

Replacing |CD| with |BC| on the RHS: 
|AB| + |BC| = |BC| + |DE|

Therefore |AB| = |DE|,  and AB is congruent to DE.