Problem 2 · 2023 Math Kangaroo
Easy
Geometry & Measurement
spatial-reasoning
Which of the following shapes cannot be cut into two trapeziums with one single straight line?
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Answer: A — triangle
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Hint 1 of 2
A trapezium has exactly one pair of parallel sides; you need a single straight cut making two of them.
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Hint 2 of 2
A straight cut through a triangle always leaves a triangle on one side, which can never be a trapezium.
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Approach: test each shape for a single line that splits it into two trapeziums
- Rectangle, square, hexagon and the trapezium can each be split by one line into two four-sided pieces, each with a pair of parallel sides.
- A triangle has only three sides; any straight cut produces a smaller triangle on one side.
- A triangle cannot become two trapeziums, so the answer is the triangle (A).
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