If △ ABC≅ △ FGH, then ∠ A ≅ ∠ F. If △ ABC ≅ △ HGF, then ∠ A ≅ H. Do you notice the importance of the order of the vertices?
When we do not have a graph, to identify the corresponding parts of two congruent triangles we use the order of the vertices. The position of each vertex gives us the congruent parts.
Practice makes perfect
Let's remember the definition of congruent polygons.
Two polygons are congruent if and only if
their corresponding parts are congruent.
When we do not have a graph, to identify the corresponding parts of two triangles we use the order of the vertices. This is why it is so important to name them correctly. For example, let's say that △ ABC ≅ △ PQR, and let's connect the vertices that have the same position.
From the congruence above, we can list the corresponding parts.
ccc
Angles: & & Sides: [0.15cm]
∠ A ≅ ∠ P & & A B ≅ P Q [0.1cm]
∠ B ≅ ∠ Q & and & B C ≅ Q R [0.1cm]
∠ C ≅ ∠ R & & A C ≅ P R
As you can see, the position of each vertex gives us the congruent parts.
Example of Incorrect Naming
Let's consider the two congruent triangles below.
Both triangles have all their corresponding parts congruent, and we must reflect this when naming them. An incorrect naming would be △ A B C ≅ △ R S T, because this would imply — for example — that ∠ A≅ ∠ R which is false. To name them correctly, we could use the angles that are congruent.
First, since ∠ A ≅ ∠ S we can write them as the first vertex: △ A ? ? ≅ △ S ? ?
Secondly, ∠ B ≅ ∠ R and so, we can write them as the second vertex: △ A B ? ≅ △ S R ?
Finally, since ∠ C ≅ ∠ T we write them as the third vertex: △ A B C ≅ △ S R T.
The main thing here is to write the congruent angles in the same position.
