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CPCTC

CPCTC

Overview
In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....

, CPCTC is the abbreviation of a theorem
Theorem
In mathematics, a theorem is a statement proved on the basis of previously accepted or established statements such as axioms. In formal mathematical logic, the concept of a theorem may be taken to mean a formula that can be derived according to the derivation rules of a fixed formal system.In...

 involving congruent
Congruence (geometry)
In geometry, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections...

 triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

s. 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, or SAS, then all of their corresponding parts are congruent as well.

If
then the following conditions are true:


A related theorem is
CPCFC, in which triangles is replaced with figures so that the theorem applies to any polygon
Polygon
In geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments . These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners...

 or polyhedron
Polyhedron
A polyhedron is often defined as a geometric solid with flat faces and straight edges .This definition of a polyhedron is not very precise, and to a modern mathematician is...

.
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Encyclopedia
In
geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....

, CPCTC is the abbreviation of a theorem
Theorem
In mathematics, a theorem is a statement proved on the basis of previously accepted or established statements such as axioms. In formal mathematical logic, the concept of a theorem may be taken to mean a formula that can be derived according to the derivation rules of a fixed formal system.In...

 involving congruent
Congruence (geometry)
In geometry, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections...

 triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

s. 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, or SAS, then all of their corresponding parts are congruent as well.

If
then the following conditions are true:


A related theorem is
CPCFC, in which triangles is replaced with figures so that the theorem applies to any polygon
Polygon
In geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments . These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners...

 or polyhedron
Polyhedron
A polyhedron is often defined as a geometric solid with flat faces and straight edges .This definition of a polyhedron is not very precise, and to a modern mathematician is...

.

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