1. The problem asks for the additional information needed to prove triangles congruent given a specific reason (ASA, SAS, or SSS) and one pair of congruent parts. 2. For each case, recall the congruence criteria: - ASA (Angle-Side-Angle): Two angles and the included side are congruent. - SAS (Side-Angle-Side): Two sides and the included angle are congruent. - SSS (Side-Side-Side): All three sides are congruent. 3. Analyze each given: 11) ASA with \(\angle SUT \cong \angle DUT\) - Given one pair of congruent angles, need the included side and the other angle congruent. - Additional info: Side \(UT \cong UT\) (common side) and \(\angle UST \cong \angle UDT\). 12) SAS with \(VW \cong XK\) - Given one pair of congruent sides, need the included angle and the other side congruent. - Additional info: \(\angle WVX \cong \angle XKW\) (included angle) and side \(WV \cong KW\). 13) SAS with \(CA \cong LJ\) - Given one pair of congruent sides, need the included angle and the other side congruent. - Additional info: \(\angle BCA \cong \angle ALJ\) (included angle) and side \(BC \cong AL\). 14) ASA with \(DE \cong JK\) - Given one pair of congruent sides, need the two angles including that side congruent. - Additional info: \(\angle E \cong \angle K\) and \(\angle D \cong \angle J\). 15) SAS with \(IJ \cong ST\) - Given one pair of congruent sides, need the included angle and the other side congruent. - Additional info: \(\angle JIH \cong \angle TST\) (included angle) and side \(JH \cong TS\). 16) ASA with \(\angle L \cong \angle T\) - Given one pair of congruent angles, need the included side and the other angle congruent. - Additional info: Side \(LK \cong TU\) (included side) and \(\angle K \cong \angle U\). 17) SSS with \(RS \cong DQ\) - Given one pair of congruent sides, need the other two pairs of sides congruent. - Additional info: \(RQ \cong DQ\) and \(SQ \cong QD\). 18) SAS with \(VW \cong VM\) - Given one pair of congruent sides, need the included angle and the other side congruent. - Additional info: \(\angle WVU \cong \angle MVU\) (included angle) and side \(WU \cong MU\). Final answer: For each case, the missing parts are the other congruent angle(s) or side(s) needed to satisfy the ASA, SAS, or SSS criteria as explained above.