Triangle Congruence

A triangle is a closed figure consisting of 3 angles and 3 sides.  The sides are segments and meet at their vertices.  We name a triangle by listing its three vertices.  Two triangles are congruent if they have the same size and shape.  In naming congruent triangles we must list the vertices in a consistent order, and we use an equals-sign with a wiggle over it.  For example, if A, B and C are the vertices of one triangle, and D, E and F are the vertices of another triangle that is congruent to the first one, then only one of the following six possible congruences can be true:

                 or    or    or

                 or    or 

Each implies a different correspondence of the vertices.  If the triangles are these:

then the correct congruence is: .  This means that vertex A of the first triangle matches vertex F of the second, vertex B of the first matches vertex D of the second, and vertex C of the first matches vertex E of the second.

 

Since congruent means the triangles have the same size and shape, it implies that six pairs of corresponding parts have the same measure, the three angle-pairs and the three side-pairs.  Thus,  implies the following six facts,

        ,    ,    ,    ,    ,   

and if all six of these are true, then the triangles are congruent. 

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