CPCTC
Encyclopedia
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 that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
involving congruent
Congruence (geometry)
In geometry, two figures are congruent if they have the same shape and size. This means that either object can be repositioned so as to coincide precisely with the other object...
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, HL, or SAS, then all of their corresponding parts are congruent as well. CPCTC is especially useful in proving various geometrical problems and theorems.
If
then the following statements are true:
A related theorem is CPCtC, in which triangles is replaced with figures so that the theorem applies to any polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
or polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
.