1. SSS: [tex]\(\overline{LK} \cong \overline{VU}\)[/tex], [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], [tex]\(\overline{LJ} \cong \overline{VT}\)[/tex]
2. SAS: [tex]\(\overline{LK} \cong \overline{VU}\)[/tex], [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], [tex]\(\angle K \cong \angle U\)[/tex]
3. ASA: [tex]\(\overline{LK} \cong \overline{VU}\)[/tex], [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], [tex]\(\angle L \cong \angle V\)[/tex].
For SSS (Side-Side-Side) congruence, have all three sides of one triangle congruent to the corresponding sides of the other triangle.
Given:
[tex]\(\overline{LK} \cong \overline{VU}\)[/tex] and [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex].
For SAS (Side-Angle-Side) congruence, two sides are needed and the included angle of one triangle congruent to the corresponding sides and the included angle of the other triangle.
Given:
[tex]\(\overline{LK} \cong \overline{VU}\)[/tex] and [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], and [tex]\(\angle K \cong \angle U\)[/tex].
For ASA (Angle-Side-Angle) congruence, two angles are needed and the included side of one triangle congruent to the corresponding angles and the included side of the other triangle.
Given:
[tex]\(\overline{LK} \cong \overline{VU}\)[/tex] and [tex]\(\overline{KJ} \cong \overline{UT}\)[/tex], and [tex]\(\angle L \cong \angle V\)[/tex].
So, the missing information for each case is:
1. SSS: [tex]\(\overline{LJ} \cong \overline{VT}\)[/tex]
2. SAS: [tex]\(\angle K \cong \angle U\)[/tex]
3. ASA: [tex]\(\angle L \cong \angle V\)[/tex].