Question

AC, DE = EC Prove: DE AE Statements 1. E is the midpoint of AC Reason...​

Answer 1

The midpoint of a line divides the line into equal halves.

The complete proof is:

1. E is the midpoint of AC -- Given
2. AE = EC --- Definition of midpoint
3. DE = EC --- Given
4. AE = DE -- Substitution property of equality
5. $\mathbf{AE \cong DE}$ --- Definition of congruence
6. $\mathbf{DE \cong AE}$ --- Proved

The given parameters (see attachment) are:

• E is the midpoint of AC
• $\mathbf{DE = EC}$.

So, the reason for the first statement is: Given.

Point E is the midpoint of AC.

So, the second statement would be:

$\mathbf{AE = EC}$

By substitution property of equality, we substitute DE for EC.

The above equation becomes:

$\mathbf{AE = DE}$

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:

$\mathbf{AE \cong DE}$ or $\mathbf{DE \cong AE}$

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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