Thread: Proving Side-Side-Side congruency of a triangle

I need to prove SSS traingle congruency using Side-Angle-Side as an axiom. I know that if 3 sides of a triangle are congruent to 3 sides of another triangle the 2 triangles are equivalent. I am just not sure how to write up in a proof using SAS as the axiom or the given. Thanks for any help anyone can give. In the question it said to use a kite or dart to help with the proof, but I do not see how that can help.

Hello, reagan3nc!

I need to prove SSS triangle congruency using SAS as an axiom.

It said to use a kite or dart to help with the proof

Code:

                      B
                      *
                  * α |β*
              *       |   *
          *           |     *
    A * - - - - - - - * - - - * C
          *           |E    *
              *       |   *
                  * α |β*
                      *
                      D

We are given two triangles with equal corresponding sides.
Place them so they have an equal side in common.

We have and with: .
. . and, of course,

Since is isosceles.
Hence, its base angles are equal: .

Since is isosceles.
Hence, its base angles are equal: .


Since . then: .


And we have: .


Therefore: .