If you want to use rigid transformation to justify the SSS congruence theorem, what type of triangles do you need to start with?

Answer 1

To use rigid transformation to justify the Side-Side-Side (SSS) congruence theorem, you need to start with two triangles that have sides of equal lengths. More specifically, you would need to take two triangles, say triangle \( ABC \) and triangle \( DEF \), such that:

• The length of side \( AB \) is equal to the length of side \( DE \).
• The length of side \( BC \) is equal to the length of side \( EF \).
• The length of side \( CA \) is equal to the length of side \( FD \).

In this case, a rigid transformation (which can include translations, rotations, and reflections) can be applied to one triangle to superimpose it onto the other triangle. This demonstrates that the two triangles are congruent because a rigid transformation preserves distance and angles.

Therefore, the type of triangles you need to start with for the SSS congruence theorem is any two triangles that have all three corresponding sides equal in length.