পুনরালোচনা: সর্বসম ত্রিভুজের বৈশিষ্ট্য

This is another way of saying $Corresponding$ $Parts$ of $Congruent$ $Triangles$ are $Congruent$, or $CPCTC$. That is, if $\triangle ABC \cong \triangle DEF$, then $\angle A \cong \angle D$ but not necessarily $\angle A \cong \angle E$.

Triangles are congruent iff all of their sides and their angles are the same. This means that corresponding parts of congruent triangles are congruent. For example, if $\triangle ABC \cong \triangle DEF$, $\angle BAC \cong \angle EDF$ but $\angle BAC \ncong \angle DEF$. This is so because vertex A corresponds to vertex D and not E. One can show what vertices correspond to each other by the order in which they write them. This applies to both sides and angles.

Extra practice can be found here.

(Video) What are the Triangle Congruence Theorems?

by MashUp Math

If two triangles are congruent, they have the same shape and size. More specifically, corresponding parts of congruent triangles are congruent, we refer to this as CPCTC. Here is an example:

We are given that $\triangle ABC\cong\triangle DEF$. Note that the order of the letters is important--the vertices should correspond to each other. For example, $A$ corresponds to $D$, meaning they are congruent; $\overline{AC}$ corresponds to $\overline{EF}$, meaing they are congruent.

Try the following problem!

We already know that in order for us to claim two triangles are congruent, we must show they have the same shape and size. However, often times it is hard to compare visually if two triangles are congruent. We need to prove that two triangles are congruent, instead of saying, "they seem like they are congruent!"

The video clip introduces 5 ways to prove triangle congruence. Don't worry if you don't understand them at this point, you will learn it soon!