Editing Congruence (geometry) (section)

=== {{anchor|CPCTC}} CPCTC===
This [[acronym]] stands for ''Corresponding Parts of Congruent Triangles are Congruent'', which is an abbreviated version of the definition of congruent triangles.<ref>{{citation |last=Jacobs |first=Harold R. |title=Geometry |url=https://archive.org/details/geometry0000jaco/page/160/mode/2up |page=160 |year=1974 |publisher=W.H. Freeman |isbn=0-7167-0456-0}} Jacobs uses a slight variation of the phrase</ref><ref>{{cite web|url=https://www.cliffsnotes.com/study-guides/geometry/triangles/congruent-triangles|title=Congruent Triangles|publisher=Cliff's Notes|access-date=2014-02-04}}</ref>
 
In more detail, it is a succinct way to say that if triangles {{mvar|ABC}} and {{mvar|DEF}} are congruent, that is,

:<math>\triangle ABC \cong \triangle DEF,</math>

with corresponding pairs of angles at vertices {{mvar|A}} and {{mvar|D}}; {{mvar|B}} and {{mvar|E}}; and {{mvar|C}} and {{mvar|F}}, and with corresponding pairs of sides {{mvar|AB}} and {{mvar|DE}}; {{mvar|BC}} and {{mvar|EF}}; and {{mvar|CA}} and {{mvar|FD}}, then the following statements are true:

:<math>\overline{AB} \cong \overline{DE}</math>
:<math>\overline{BC} \cong \overline{EF}</math>
:<math>\overline{AC} \cong \overline{DF}</math>
:<math>\angle BAC \cong \angle EDF</math>
:<math>\angle ABC \cong \angle DEF</math>
:<math>\angle BCA \cong \angle EFD.</math>

The statement is often used as a justification in elementary geometry proofs when a conclusion of the congruence of parts of two triangles is needed after the congruence of the triangles has been established. For example, if two triangles have been shown to be congruent by the ''SSS'' criteria and a statement that corresponding angles are congruent is needed in a proof, then CPCTC may be used as a justification of this statement.

A related theorem is '''CPCFC''', in which "triangles" is replaced with "figures" so that the theorem applies to any pair of [[polygon]]s or [[polyhedron]]s that are congruent.