Explain how proving two triangles
congruent can help prove parts of
the triangle congruent.
Proving two triangles congruent means showing that all corresponding sides and angles of the two triangles are equal. This can help prove parts of the triangles congruent because once we have shown the whole triangles are congruent, we can then conclude that their corresponding parts are also congruent.
For example, if we have two triangles ABC and DEF and we have shown that triangle ABC is congruent to triangle DEF, we can then say that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. We can also say that side AB is congruent to side DE, side AC is congruent to side DF, and side BC is congruent to side EF.
Therefore, by proving two triangles congruent, we can use that information to prove specific parts of the triangles congruent as well.