1. **Problem Statement:** Determine the relationship between given line segments and planes in a cube, and identify angle pairs using the provided word bank. 2. **Line Relationships in Cube:** - Lines are either parallel, perpendicular, or skew. - Parallel lines lie in the same plane and never intersect. - Perpendicular lines intersect at a 90° angle. - Skew lines do not intersect and are not parallel (they lie in different planes). 3. **Answers for Line Relationships:** - a) $\overline{AB}$ and $\overline{DH}$ are **parallel** lines because they are edges of the cube running in the same direction. - b) $\overline{DC}$ and $\overline{HG}$ are **parallel** lines for the same reason. - c) $\overline{BF}$ and $\overline{EF}$ are **perpendicular** lines because they meet at a right angle on the cube. - d) Plane ABC and GHE are **parallel** planes because they are opposite faces of the cube. 4. **Angle Pair Definitions:** - Alternate Exterior (A): Angles on opposite sides of the transversal and outside the two lines. - Alternate Interior (B): Angles on opposite sides of the transversal and inside the two lines. - Consecutive Interior (C): Angles on the same side of the transversal and inside the two lines. - Consecutive Exterior (D): Angles on the same side of the transversal and outside the two lines. - Corresponding (E): Angles in the same relative position at each intersection. - Linear Pair (F): Adjacent angles that form a straight line. - Vertical Pair (G): Opposite angles formed by two intersecting lines. - No relationship (H): Angles that do not fit any of the above. 5. **Angle Pair Answers:** - a) $\angle 1$ and $\angle 5$ are **Corresponding (E)** because they are in the same relative position at different intersections. - b) $\angle 1$ and $\angle 3$ are **Vertical Pair (G)** because they are opposite angles formed by intersecting lines. - c) $\angle 2$ and $\angle 5$ are **Alternate Interior (B)** because they lie between the two lines on opposite sides of the transversal. - d) $\angle 2$ and $\angle 7$ are **Alternate Exterior (A)** because they lie outside the two lines on opposite sides of the transversal. - e) $\angle 6$ and $\angle 4$ are **Alternate Interior (B)**. - f) $\angle 2$ and $\angle 8$ are **Corresponding (E)**. - g) $\angle 7$ and $\angle 8$ are **Linear Pair (F)** because they are adjacent and form a straight line. - h) $\angle 4$ and $\angle 5$ have **No relationship (H)**. Final answers: 1a) Parallel 1b) Parallel 1c) Perpendicular 1d) Parallel 2a) Corresponding 2b) Vertical Pair 2c) Alternate Interior 2d) Alternate Exterior 2e) Alternate Interior 2f) Corresponding 2g) Linear Pair 2h) No relationship