Given: AB=CD Prove: AC=BD

Question

I am so confused with proofs :(

Can someone please explain?

Answer 1

I am assuming that you have a single line segment AD with points B and C on it so that AB = CD. 

Let's say AB = 14 = CD. Let's also choose BC, the middle segment, equal 6. What would the lengths of AC and BD come out to be?

     AC = AB + BC = 14 + 6 = 20

     BD = CD + BC = 14 + 6 = 20

 

Do you see why regardless of the values you pick, these sums will always be equal?

You know AB = CD because it was given as true,

You know BC = BC because of the reflexive postulate,

So you know AB+BC = CD + BC because of the addition postulate.

Some teachers get very technical and say AB+BC=AC and CD+BC=BD from the partition postulate, and then you can use the substitution postulate to get your final statement AC=BD.

 

Hope this helps.