EDGE Math 8

Congruent Triangles

Definition

Congruent triangles are triangles with corresponding sides having the same length and with corresponding angles having the same measure.

From the given definition of congruent triangles, the congruence of the corresponding parts of triangles follows. For convenience, you may use the acronym CPCTC to mean "Corresponding Parts of Congruent Triangles are Congruent."

Refer to the figure below.

Suppose that $Δ A B C$ can be made to coincide with $Δ G E O,$ then $Δ A B C ≅ Δ G E O .$ The vertices of the two triangles correspond in the same order as the letters naming the triangles. For example, the expression "vertex A corresponds to vertex G," is denoted by $A \leftrightarrow G .$

The correspondences of the vertices of $Δ A B C$ and $Δ G E O$ are denoted as follows:

A \leftrightarrow G,

B \leftrightarrow E,

and

C \leftrightarrow O .

Hence, $Δ A B C ≅ Δ G E O .$