Question

Explain how proving two triangles congruent can help prove parts of the triangle congruent.

Answer 1

Explanation:

If two triangles are congruent, this means they are the same shape and the same size.

By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

When we know that two triangles are congruent and are showing that corresponding sides or corresponding angles of the triangles are congruent, we use the justification "CPCTC". This stands for:

Corresponding

Parts of

Congruent

Triangles are

Congruent.

Answer 2

Firstly, you can't just say that two triangles are congruent without any given sides or angles that you can prove to be congruent. Sides and angles have to be given in order to proves that triangles are congruent. For example, you need three sides of each triangle to be congruent for the SSS (Side-Side-Side) Triangle Congruence Theorem to take place. Same for other theorems such as SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or Hypotenuse Leg. Only proving that one of these theorems are in place can you prove two triangles, and all of its parts, to be congruent. Once you prove that the triangles are congruent using one of these theorems you can use CPCTC (Corresponding Parts of Congruent Triangles are Congruent).


*Sorry if I made this sound confusing but if you have any further questions, please feel free to ask! I'd be happy to help anytime!