To draw a cross section, you can sometimes use the idea from Postulate 1-3 that the intersection of two planes is exactly one line.
Visualization Draw a cross section formed by a vertical plane intersecting the front and right faces of the cube. What shape is the cross section?
How can you see parallel segments?
Focus on the plane intersecting the front and right faces. The plane and both faces are vertical, so the intersections are vertical parallel lines.
Step 1
Visualize a vertical plane intersecting the vertical faces in parallel segments.
Step 2
Draw the parallel segments.
Step 3
Join their endpoints. Shade the cross section.
The cross section is a rectangle.
How many faces, edges, and vertices are in the solid? List them.
What is the cross section formed by the cube and the plane containing the diagonals of a pair of opposite faces?
Error Analysis Your math class is drawing polyhedrons. Which figure does not belong in the diagram below? Explain.