# Geometry proofs

1. Sep 28, 2008

### Taylorrr8394

Given : line AD is congruent to line BE

Prove: line AE is congruent to line BD

2. Sep 28, 2008

### tiny-tim

Welcome to PF!

Hi Taylorrr8394! Welcome to PF!
But that obviously isn't true

Have you left something out?

What are A B D and E (and whatever happened to poor little C? )

3. Oct 1, 2008

### jth01

Why isn't it?

If line AD is congruent to line BE, doesn't that mean they are the same line, so then any two pair of lines made of those letters (line AB, line AD, line AE, line BD, line BE, line DE) are also describing the same line and thus congruent? Am I missing something?

4. Oct 1, 2008

### tiny-tim

Hi jth01!

Perhaps your book is using a different definition of "congruent".

The definition I was taught is that two lines are congruent if they are the same length … but they can be at any place, and in any direction.

5. Oct 3, 2008

### jth01

Doesn't a line have infinite length?

6. Oct 4, 2008

### tiny-tim

line segment

Hi jth01!

hmm … interesting point!

I agree that "a line", on it own, must be infinite, and a finite part of a line is "a line segment".

But if particular points are specified, to name the line, then standard usage is that "the line through A and B" is infinite,

but "the line AB" is the line segment.