∠CAR and ∠BCR are included angles

∠ACR and ∠BCR are included angles

∠ACR ≅ ∠BCR

∠ACR > ∠BCR

Given

Congruence Theorem

Hinge Theorem

Converse of Hinge Theorem

BC≅BC

CR ≅ CR

AR > BR

∠CRA<∠CRB

CR ≅ CR

AR< BR

∠ACR < ∠BCR

∠ACR < ∠BRC

CR ≅ CR

AC ≅ BC

∠ACR < ∠BCR

AR < BR

Hinge Theorem

Converse of Hinge theorem

SSS Inequality Theorem

ASA Inequality Theorem