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

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MrRoyalidn

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. [tex]\mathbf{AE \cong DE}[/tex] --- Definition of congruence
  6. [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:

https://brainly.com/question/4435557

View image MrRoyal
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