Question

which figures have a triangle cross - section? choose all that apply.
□ a.
□ b.
□ c.
□ d.
□ e.

Explanation:

• Figure A (a square pyramid): A cross-section cut parallel to its base is a square, but a cut through the apex and two opposite base vertices creates a triangular cross-section.
• Figure B (a triangular prism): A cross-section cut parallel to its triangular bases will be a triangle.
• Figure C (a cube): Any cross-section will be a quadrilateral, triangle, or other polygon, but a cut through three adjacent vertices creates a triangular cross-section.
• Figure D (a cone): All cross-sections through the apex are triangles, while parallel cuts are circles.
• Figure E (a cylinder): Cross-sections are either circles (parallel to bases) or rectangles (perpendicular to bases), no triangular cross-sections possible.

Answer:

A. Square Pyramid, B. Triangular Prism, C. Cube, D. Cone