Rolling resistance

Two congruent triangles

Two congruent triangles

In geometry, '"Corresponding parts of congruent triangles are congruent"' is the abbreviation of a Theorem involving congruent triangles. CPCTC states that if two or more triangles are proven congruent by any method (including but not limited to SSS, SAS, AAS, ASA) then all of their corresponding angles and sides are congruent as well. CPCTC is especially useful in proving various geometrical triangles and polygons.

If:

$\mathrm{△}ABC\cong \mathrm{△}DEF$

then the following statements are true:

$\overline{AB}\cong \overline{DE}$

$\overline{BC}\cong \overline{EF}$

$\overline{AC}\cong \overline{DF}$

$\mathrm{\angle }BAC\cong \mathrm{\angle }EDF$

$\mathrm{\angle }ABC\cong \mathrm{\angle }DEF$

$\mathrm{\angle }BCA\cong \mathrm{\angle }EFD.$

A related theorem is CPCFC, in which triangles is replaced with figures so that the theorem applies to any polygon or polyhedron proven congruent.

External links

• Dr. Math explains the importance of CPCTC

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