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2021 Math Kangaroo

Problem 9

Problem 9 · 2021 Math Kangaroo Medium
Spatial & Visual Reasoning gridspatial-reasoning
Figure for Math Kangaroo 2021 Problem 9
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Answer: D
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Hint 1 of 2
First read off the two shown triangles: count their areas, which are isosceles, and which are right-angled.
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Hint 2 of 2
The third triangle has to make each of the three counts land on exactly two — same area, isosceles, right-angled — so test every option against all three at once.
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Approach: make each of the three counts (equal area, isosceles, right-angled) equal exactly two
  1. Read the two given triangles from the grid: note each one's area, whether it is isosceles, and whether it has a right angle.
  2. The third triangle must push each count to exactly two: exactly two of equal area, exactly two isosceles, exactly two right-angled.
  3. Check each option against all three conditions together — most options break at least one of the counts.
  4. Only the triangle in choice (D) satisfies all three at once.
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