Explain how proving two triangles congruent can help prove parts of the triangle congruent.
Proving two triangles congruent can help prove parts of the triangles congruent through the use of corresponding parts of congruent triangles (CPCTC). If two triangles are proven to be congruent, then their corresponding parts (sides and angles) are also congruent.
For example, if two triangles are proven to be congruent by the SAS (Side-Angle-Side) criteria, then the corresponding sides and angles of the triangles are congruent. This means that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the remaining angles and sides of the triangles are also congruent.
By using the CPCTC property, we can then conclude that other parts of the triangles are congruent. This can help us prove various properties of triangles, such as the congruence of angles, sides, or entire triangles.