Proving Congruence of Line AE and BD

[Taylorrr8394]

Given : line AD is congruent to line BE

Prove: line AE is congruent to line BD

please help! i have no idea what to doo!

 

[tiny-tim]

Welcome to PF!

Hi Taylorrr8394! Welcome to PF!

Given : line AD is congruent to line BE

Prove: line AE is congruent to line BD

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? )

 

[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?

 

[tiny-tim]

Why isn't it?

If line AD is congruent to line BE, doesn't that mean they are the same line …

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.

 

[jth01]

Doesn't a line have infinite length?

 

[tiny-tim]

line segment

Doesn't a line have infinite length?

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.