1. **Problem Statement:** We have two index cards labeled with points A, B, C, D, E, F, G, M, N and lines AB, CD, EF, and planes M and N. We need to find intersections of lines and planes before and after sliding the cards together, and determine if lines CD and EF are coplanar. 2. **Step 1: When the cards are NOT together:** - Intersection of lines AB and CD: Since AB is the diagonal cut from A to B and CD is a vertical edge from C to D, these lines intersect at point G, the intersection of the perpendicular lines inside the rectangle. - Intersection of lines AB and EF: EF is a line on the second card. Since the cards are separate, AB and EF lie on different cards and do not intersect. So, the intersection is the empty set $\emptyset$. 3. **Step 2: With the cards together:** - Intersection of lines CD and EF: When the cards slide together, lines CD and EF intersect at point G, where the two cards overlap and the lines cross. 4. **Step 3: Intersection of planes M and N:** Planes M and N are the planes of the two cards. Their intersection is the line along which the cards slide together, which is line AB. 5. **Step 4: Are lines CD and EF coplanar?** Since CD lies on plane N and EF lies on plane M, and the planes intersect along line AB, lines CD and EF lie in different planes but intersect at point G. Two lines intersecting at a point are coplanar because a plane can be defined by two intersecting lines. Therefore, CD and EF are coplanar. **Final answers:** - Intersection of AB and CD: point $G$ - Intersection of AB and EF: $\emptyset$ - Intersection of CD and EF (cards together): point $G$ - Intersection of planes M and N: line $AB$ - Lines CD and EF are coplanar because they intersect at $G$.