CPCTC

In geometry, CPCTC is the abbreviation of a theorem involving congruent triangles. CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. CPCTC states that if two or more triangles are proven congruent by: ASA, AAS, SSS, HL, or SAS, then all of their corresponding parts are congruent as well. CPCTC is especially useful in proving various geometrical problems and theorems.

If

$\triangle ABC \cong \triangle DEF\,$

then the following statements are true:

$\overline{AB} \cong \overline{DE}\,$

$\overline{BC} \cong \overline{EF}\,$

$\overline{AC} \cong \overline{DF}$

$\angle BAC \cong \angle EDF\,$

$\angle ABC \cong \angle DEF\,$

$\angle BCA \cong \angle EFD.\,$

A related theorem is CPCtC, in which triangles is replaced with figures so that the theorem applies to any polygon or polyhedron.

External links

• Dr. Math explains the importance of CPCTC