Answered

From beginner to expert, IDNLearn.com has answers for everyone. Ask anything and receive thorough, reliable answers from our community of experienced professionals.

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

Sagot :

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
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.