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.



 

Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
 .





In order for the problem's formulation be correct and accurate, it should say that all the points lie in one straight line.







 

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