1. **Problem Statement:** Determine if the given pairs of triangles are congruent and by which congruence criterion (SSS, SAS, ASA, AAS, or not necessarily congruent). 2. **Important Rules:** - **SSS (Side-Side-Side):** Triangles are congruent if all three sides of one triangle are equal to the corresponding three sides of the other. - **SAS (Side-Angle-Side):** Triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of the other. - **ASA (Angle-Side-Angle):** Triangles are congruent if two angles and the included side are equal. - **AAS (Angle-Angle-Side):** Triangles are congruent if two angles and a non-included side are equal. --- ### (a) Triangles MNO and PQR - Given: Segments MO = RP and ON = PQ, and each triangle has one right angle. - Since each triangle has a right angle, and two sides adjacent to the right angle are equal respectively, this is SAS congruence (Side-Angle-Side). ### (b) Triangles ABC and DEF - Given: Segments AC = DE and BC = EF. - No information about angles or the third side. - Without the third side or an angle, congruence is **not necessarily guaranteed**. ### (c) Triangles UVW and XYZ - Given: Segments UV = XY and UW = XZ, and two equal angles marked in each triangle. - Two sides and two angles are equal. - If the angle between the two sides is equal, then SAS applies. - Since two angles and two sides are equal, the triangles are congruent by SAS or possibly ASA depending on which angles are equal. --- **Final answers:** - (a) $\triangle MNO \cong \triangle PQR$ by SAS. - (b) Not necessarily congruent. - (c) $\triangle UVW \cong \triangle XYZ$ by SAS.