1. **Problem Statement:** Determine whether the given pairs of lines in the tetrahedron are intersecting, perpendicular, parallel, or skew. 2. **Recall definitions:** - Intersecting lines meet at a point. - Perpendicular lines intersect at a 90° angle. - Parallel lines lie in the same plane and never meet. - Skew lines do not intersect and are not parallel (they lie in different planes). 3. **Analyze each pair:** 1. $\overleftrightarrow{BA}$ and $\overleftrightarrow{CD}$: Both lie in the base plane (since A, B, C, D are coplanar). They intersect at point $D$ or $B$? Actually, $BA$ connects points B and A, $CD$ connects points C and D. Since ABCD is a base plane quadrilateral, lines $BA$ and $CD$ intersect if their segments cross. In a tetrahedron base, $BA$ and $CD$ are opposite edges and do not intersect. So they are not intersecting lines. Answer: F 2. $\overleftrightarrow{BA}$ and $\overleftrightarrow{CD}$ perpendicular? Since they do not intersect, they cannot be perpendicular. Answer: F 3. $\overleftrightarrow{EB}$ and $\overleftrightarrow{CD}$: $EB$ connects vertex E (above base) to B (on base), $CD$ is on base. They lie in different planes and do not intersect. Are they parallel? No, because they are not in the same plane. Answer: F 4. $\overleftrightarrow{AB}$ and $\overleftrightarrow{DC}$ skew lines? $AB$ and $DC$ are edges on the base plane, so they lie in the same plane. Since they do not intersect and are not parallel, they are not skew. Answer: F 5. $\overleftrightarrow{CA}$ and $\overleftrightarrow{BD}$ parallel lines? Both are edges on the base plane. In a tetrahedron base, $CA$ and $BD$ are opposite edges and do not intersect. Are they parallel? Yes, opposite edges in a quadrilateral can be parallel. Answer: T 6. $\overleftrightarrow{BA}$ and $\overleftrightarrow{EC}$ skew lines? $BA$ is on base plane, $EC$ connects E (above base) to C (on base). They do not intersect and are not parallel, and lie in different planes. So they are skew. Answer: T **Final answers:** 1. F 2. F 3. F 4. F 5. T 6. T