CPCTC

In geometry, "Corresponding parts of congruent triangles are congruent" (CPCTC) is the abbreviation of a theorem regarding congruent triangles.[1] CPCTC states that if two or more triangles are proven congruent by any method, then all of their corresponding angles and sides are congruent as well. CPCTC is especially useful in proving various geometrical triangles and polygons.[2]

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 CPCFC, in which "triangles" is replaced with "figures" so that the theorem applies to any polygon or polyhedron proven congruent.

References

  1. ↑ "Congruent Triangles". Cliff's Notes. Retrieved 2014-02-04.
  2. ↑ "CPCTC means 'Corresponding parts of congruent triangles are congruent' and...". Mathware House. Retrieved 2014-02-04.

External links