In
geometryGeometry 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
theoremIn 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
congruentIn 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...
triangleA 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 C
orresponding P
arts of C
ongruent T
riangles are C
ongruent. 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
polygonIn 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
polyhedronA 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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In
geometryGeometry 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
theoremIn 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
congruentIn 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...
triangleA 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 C
orresponding P
arts of C
ongruent T
riangles are C
ongruent. 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
polygonIn 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
polyhedronA 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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