Abbreviation for Corresponding Parts Of Congruent Triangles are Congruent. An important principle used in plane geometry for proving that lines or angles are equal. Just prove that they're corresponding parts of congruent triangles, and let CPCTC do the rest.

Example:

Prove: If the bisector of the vertex angle         B
       of a triangle is perpendicular to           ^
       the base, it bisects the base.             /|\
Given: In Δ ABC, BD bisects angle ABC,           /3|4\
       BD is perpendicular to AC.               /  |  \
To Prove: AD = DC                              /__1|2__\
                                              A    D   C

   Statements                           Reasons

1. BD bisects angle ABC              1. Given.
2. ∠ 3 = ∠ 4                       2. To bisect is to divide into equal parts.
3. BD is perpendicular to AC         3. Given.
4. ∠s 1 and 2 are right angles      4. Perpendicular lines meet at right angles.
5. ∠ 1 = ∠ 2                       5. All right angles are equal.
6. BD = BD                           6. Identity.
7. Δ ABD is congruent to Δ CBD       7. A-S-A
8. AD = DC                           8. CPCTC
   

Log in or registerto write something here or to contact authors.