Download Exploring Congruent Triangles

Exploring Congruent Triangles

Congruent Triangles (CPCTC)-two triangles are congruent if and only if their
corresponding parts are congruent (Congruent Parts of Congruent Triangles Are
Congruent).
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Parts of congruent triangles-each triangle has three angles and three sides
any of which may be congruent. If the corresponding six parts of one
triangle are congruent to the six parts of another triangle, then the triangles
are congruent.

Theorem 4-4-congruence of triangles is reflexive, symmetric, and transitive
Example:
In the figure below,  DEF is congruent to  ABC. If you slide  DEF up and to the
right,  DEF is still congruent to  ABC.
F
C
A
B
D
E
Also, if you rotate  DEF,  DEF remains congruent to  ABC.
If you flip  DEF,  DEF remains congruent.
If you slide, rotate, or flip a figure, congruence will not change. These three
transformations are called congruence transformations.
If  DEF is congruent to  ABC, the vertices of the two triangles correspond in the same
order as the letters naming the triangles.
D A
E B
F C
This correspondence of vertices can be used to name the corresponding congruent sides
and angles of the two triangles.
<D  <A
<E  <B
<F  <C
DE  AB
EF  BC
FD  CA
The corresponding sides and angles can be determined from any congruence statement by
following the order of the letters. It is important that you list the letters of the vertices in
the correct order whenever you write a congruence statement.