1. **Stating the problem:** Identify the relationships between pairs of lines and pairs of angles in the given 3D figure and trapezoid. 2. **Lines pairs:** - AB and CD: AB is a front bottom edge, CD is a back interior edge; these are parallel lines in the prism. - DF and FI: These edges intersect inside the prism, so they are intersecting lines. - EF and GH: Both are slanted top edges and parallel. - EH and CD: These are skew lines (not parallel, not intersecting). - CG and CD: CG is perpendicular to CD. 3. **Angle pairs and their lines/transversal:** - ∠1 and ∠3: These are alternate interior angles formed by lines TU and EN with transversal TN. - ∠2 and ∠4: These are corresponding angles formed by lines TU and EN with transversal TN. - ∠U and ∠UNE: These are adjacent angles sharing vertex U on lines TU and UN. - ∠5 and ∠UNE: ∠5 is an exterior angle at E, ∠UNE is interior; lines ET and EN with transversal UN. - ∠5 and ∠ETU: ∠5 is exterior at E, ∠ETU is interior at T; lines ET and EN with transversal TU. 4. **Summary:** - Lines AB and CD are parallel. - Lines DF and FI intersect. - Lines EF and GH are parallel. - Lines EH and CD are skew. - Lines CG and CD are perpendicular. - Angle pairs 1 & 3 and 2 & 4 are formed by lines TU and EN with transversal TN. - Angles U and UNE share vertex U. - Angles 5 and UNE, 5 and ETU involve exterior and interior angles with lines ET, EN, and transversal TU or UN.