Geometry Chapter 4.2 Congruence and Triangles
A) When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.
Example: Given Δ ABC is congruent to Δ PQR then we know
1) angle A = angle P, angle B = angle Q, and angle C = angle R
2) AB = PQ, BC = QR, and AC = PR
Make sure that you list the corresponding angles in the same order with the triangle congruence.
Example: ΔABC = ΔDEF is not the same as ΔABC = ΔEFD.
B) Third Angles Theorem - if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
C) Reflexive Postulate - Every triangle is congruent to itself
D) Symmetric Postulate - If ΔABC = ΔDEF, then ΔDEF = ΔABC
E) Transitive Postulate - If ΔABC = ΔDEF and ΔDEF = ΔJKL, then ΔABC = ΔJKL