Side Side Side proof

[jessica098]

I am needing help proving the Side Side Side congruence condition, which states that "if the vertices of two triangles are in one-to-one correspondence such that all three sides of one triangle are congruent, respectively, to all three sides of the second triangle, then the triangles are congruent".

What I think I have to do is use a proof by contradiction, and to start by saying to consider triangles ?ABC and ?DEF such that side AB is congruent to side DE, side AC is congruent to side DF and side BC is congruent to side EF.

I know that if two corresponding angles of the triangles are congruent, then we'd be done, by Side Angle Side. So, i would like to prove that one angle of one triangle is greater than the corresponding angle of the other triangle.

Can someone please help me do this?? Thanks!

 

[Deleted member 4993]

I am needing help proving the Side Side Side congruence condition, which states that "if the vertices of two triangles are in one-to-one correspondence such that all three sides of one triangle are congruent, respectively, to all three sides of the second triangle, then the triangles are congruent".

What I think I have to do is use a proof by contradiction, and to start by saying to consider triangles ?ABC and ?DEF such that side AB is congruent to side DE, side AC is congruent to side DF and side BC is congruent to side EF.

I know that if two corresponding angles of the triangles are congruent, then we'd be done, by Side Angle Side. So, i would like to prove that one angle of one triangle is greater than the corresponding angle of the other triangle.

Can someone please help me do this?? Thanks!

This is one of the fundamental theorems of Euclid - any textbook of geometry will have this proof included.

You could do a little bit of google search and find ~1000 sites with proof of this theorem.

One such site is:

http://www.jimloy.com/geometry/congrue0.htm