**. 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.**

__C__orresponding__P__arts Of__C__ongruent__T__riangles are__C__ongruentExample:

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