Two triangles are congruent if their corresponding sides and angles are equal. Which of the following statements is **NOT** a valid criterion for triangle congruence?

Three classical congruence criteria are valid: **SSS**, **SAS**, and **ASA**. (A fourth, **AAS**, also works.) **SSA — "two sides and a non-included angle" — is NOT a valid congruence criterion**. The given data can correspond to two different triangles (the so-called *ambiguous case*), particularly when the angle is opposite the shorter of the two given sides. Classic counter-example: with $AB = 7$, $AC = 5$, and $\angle B = 30^{\circ}$, two distinct triangles can satisfy the conditions — one with $C$ on one side of the relevant arc, one on the other. So the *invalid* criterion is **D**. The ETS Math Review explicitly lists SSS, SAS, and ASA as the standard propositions and notes that other combinations may not uniquely determine the triangle.