Problem 3 · 2023 Math Kangaroo
Easy
Spatial & Visual Reasoning
paper-cutting
Which of the shapes cannot be split into two triangles using a single straight line?
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Answer: A
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Hint 1 of 2
A single straight cut makes two pieces; to get two triangles each piece must end up with exactly three sides.
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Hint 2 of 2
Count the sides: a four-sided shape can be cut corner-to-corner into two triangles, but a six-sided one cannot.
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Approach: see which shapes a single cut can split into two triangles
- The rectangle, trapezoid and square each have four sides, so a diagonal cut turns them into two triangles.
- The triangle can be split into two triangles by a line from a vertex to the opposite side.
- The hexagon has six sides; one straight cut cannot reduce it to two three-sided pieces.
- So the shape that cannot be split is the hexagon, A.
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