Problem 3 · Do the experiment in your head · 3 points
Made by AI and not reviewed by a real person.
Zoe cuts a square sheet of paper into two pieces with ONE straight cut. Which of these can she NOT get?
- two squares
- two rectangles
- two triangles
- two trapezoids
- a triangle and a pentagon
Show a hint
- Imagine each cut: corner to corner, edge to edge straight across, edge to edge slanted…
Show the answer and solution
Answer: A — two squares
Corner-to-corner gives two triangles. A straight cut across the middle gives two rectangles. A cut from one edge to a neighboring edge gives a triangle and a pentagon. A slanted cut between opposite edges gives two trapezoids. But two squares is impossible: the two pieces would be squares joined along the whole cut line — and two squares glued edge-to-edge make a LONG rectangle, never the square you started with. Testing each option with a mental experiment is real mathematical thinking.