geometry proof??? need help?

Question

Given: segment AB=segmentAE, segment BC= Segment ED

Prove: AC = AD

Answer 1

First, draw out your diagram:

D ----- E ------ A ----- B ----- C
(all these points are equal lengths apart)

1. AB = AE ; BC = ED (Reason: Given)
2. AB + BC = AC (Reason: Segment Addition Postulate)
3. AE + DE - AD (Reason: Segment Addition Postulate)
4. AB + BC = AD (Reason: Transitive Property or Substitution Property)
5. AD = AC (Reason: Transitive Property or Substitution Property)

This is the complete proof, hope it helped!

Answer 2

D-----E------A------B------C

Here is your sketch of the problem. AE + ED = AD and AB + BC = AC

Using substitution, I can say AB + BC = AD and AE + ED = AC (since I can interchange segments of equal measure).

Now, since I "flip-flopped" the addends, I can set the sums equal to one another so AD must equal AC.

Very informal proof but you can probably formalize it easily enough.

Answer 3

We need a diagram and/or more info.
Will check back later.

If angle ABC = angle AED, then you can use SAS
If they are all on the same line, Sage B pretty much solved it for you.

Answer 4

A one-liner.
Equals subtracted from equals are equal.