The midpoint of a line divides the line into equal halves.
The complete proof is:
- E is the midpoint of AC -- Given
- AE = EC --- Definition of midpoint
- DE = EC --- Given
- AE = DE -- Substitution property of equality
- [tex]\mathbf{AE \cong DE}[/tex] --- Definition of congruence
- [tex]\mathbf{DE \cong AE}[/tex] --- Proved
The given parameters (see attachment) are:
- E is the midpoint of AC
- [tex]\mathbf{DE = EC}[/tex].
So, the reason for the first statement is: Given.
Point E is the midpoint of AC.
So, the second statement would be:
[tex]\mathbf{AE = EC}[/tex]
By substitution property of equality, we substitute DE for EC.
The above equation becomes:
[tex]\mathbf{AE = DE}[/tex]
So, the fourth reason would be: substitution property of equality
By definition of congruence, we change the equality sign to congruence equation sign
So, the fifth statement would be:
[tex]\mathbf{AE \cong DE}[/tex] or [tex]\mathbf{DE \cong AE}[/tex]
The above congruence equation shows that the statement has been proved.
So, the last reason would be Proved
Read more about proof of congruence at:
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