Prove triangles congruent

What you'll learn

1. State and explain the biconditional: two triangles are congruent (via rigid motions) if and only if all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent
2. Prove the forward direction: if two triangles are congruent (a rigid motion maps one to the other), then all corresponding pairs of sides and angles are congruent
3. Prove the reverse direction: if all corresponding pairs of sides and angles are congruent, then a sequence of rigid motions can be constructed that maps one triangle onto the other
4. Apply the principle of Corresponding Parts of Congruent Triangles are Congruent (CPCTC) to deduce side and angle congruences from established triangle congruence
5. Construct an explicit rigid-motion sequence mapping one triangle onto a congruent triangle, given corresponding vertex pairs

Prerequisites

• Use rigid motions for congruence