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#REDIRECT [[Congruence (geometry)#CPCTC]] |
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[[Image:Congruent triangles.png|right|Two congruent triangles]] |
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In [[geometry]], '''"Corresponding parts of congruent triangles are congruent"''' ('''CPCTC''') is a succinct statement of a theorem regarding [[congruence (geometry)|congruent]] [[trigonometry]], defined as triangles either of which is an [[isometry]] of the other.<ref>{{cite web|url=http://www.cliffsnotes.com/math/geometry/triangles/congruent-triangles|title=Congruent Triangles|publisher=Cliff's Notes|accessdate=2014-02-04}}</ref> CPCTC states that if two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well. CPCTC is useful in proving various theorems about triangles and other polygons.<ref>{{cite web|url=http://www.mathwarehouse.com/geometry/congruent_triangles/congruent-parts-CPCTC.php|title=CPCTC means 'Corresponding parts of congruent triangles are congruent' and...|publisher=Mathware House|accessdate=2014-02-04}}</ref> |
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If triangles ABC and DEF are congruent, denoted as |
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:<math>\triangle ABC \cong \triangle DEF,</math> |
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with corresponding pairs of angles at vertices A, D; B, E; and C, F, and with corresponding pairs of sides AB, DE; BC, EF; and CA, FD, then the following statements are true: |
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:<math>\overline{AB} \cong \overline{DE}</math> |
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:<math>\overline{BC} \cong \overline{EF}</math> |
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:<math>\overline{AC} \cong \overline{DF}</math> |
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:<math>\angle BAC \cong \angle EDF</math> |
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:<math>\angle ABC \cong \angle DEF</math> |
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:<math>\angle BCA \cong \angle EFD</math> |
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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. |
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==References== |
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{{Reflist}} corresponding parts of congruent triangles are congruent |
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==External links== |
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*[http://mathforum.org/library/drmath/view/55397.html Dr. Math explains the importance of CPCTC] |
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[[Category:Theorems in geometry]] |
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[[Category:Triangle geometry]] |
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{{elementary-geometry-stub}} |
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Latest revision as of 17:38, 20 October 2018
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