Question

which figures have a triangle cross - section? choose all that apply.
figures: a (pyramid), b (frustum), c (cube), d (cone), e (cylinder), each with a checkbox

Explanation:

• Figure A (Pyramid): A pyramid with a polygonal base (here, likely a square or triangular base) can have a triangular cross - section when cut by a plane that passes through the apex and two adjacent vertices of the base.
• Figure B (Frustum of a Pyramid): A frustum is a portion of a pyramid between two parallel planes. If we consider the original pyramid from which it is derived, a plane cutting through the frustum in a way that connects the apex (of the original pyramid) and two points on the upper base can give a triangular cross - section.
• Figure D (Cone): A cone has a circular base and an apex. A plane that passes through the apex and intersects the base (the intersection with the base is a diameter or a chord) will result in a triangular cross - section (an isosceles triangle with the two equal sides being the slant heights from the apex to the points on the base and the base of the triangle being the chord or diameter of the circular base).
• Figure C (Cube): Any cross - section of a cube will be a polygon like a square, rectangle, or hexagon, but not a triangle. Because all the faces of a cube are rectangles (squares) and the angles between the faces are right angles, a plane cutting through a cube cannot form a triangle.
• Figure E (Cylinder): A cylinder has two circular bases and a curved lateral surface. A cross - section of a cylinder is either a circle (parallel to the bases) or a rectangle (perpendicular to the bases) or an ellipse (at an angle), but never a triangle.

Answer:

A. Pyramid, B. Frustum of a Pyramid, D. Cone