Group the given figures into three classes using each figure only once.
2024
Group the given figures into three classes using each figure only once.
- A.
7,8,9 ; 2,4,3 ; 1,5,6
- B.
1,3,2 ; 4,5,7 ; 6,8,9
- C.
1,6,8 ; 3,4,7 ; 2,5,9
- D.
1,6,9 ; 3,4,7 ; 2,5,8
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Concept
To classify a set of plane figures, look for a single shared, countable property and sort by it. The most reliable property for closed line-figures is the number of straight sides (equivalently, the number of vertices): a closed figure with 3 sides is a triangle, with 4 sides a quadrilateral, and with 5 sides a pentagon. Concavity (an inward dent) does not change the side count; only the number of edges matters.
Application
Count the sides of every figure (1 to 9) and place each into a side-count bucket:
Number of sides | Figures |
|---|---|
3 sides (triangle) | 1, 6, 9 |
4 sides (quadrilateral) | 3, 4, 7 |
5 sides (pentagon) | 2, 5, 8 |
Watch the easy-to-miss figures:
Figure 3 has a small extra bend on its lower edge, so it is a four-sided figure, not a triangle.
Figure 5 is a concave arrow, but it still has exactly five edges, so it is five-sided.
Figure 8 is a notched shape, but it also has exactly five edges, so it is five-sided.
Cross-check
Each of the nine figures is used exactly once and every group is internally uniform in its number of sides, so the three classes are: triangles {1, 6, 9}, four-sided figures {3, 4, 7}, and five-sided figures {2, 5, 8}.