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How many triangles are there in the given figure?
6
7
8
9
8
Divide the square into four outer corners and the central diamond; identify the triangles formed by dividing the corner segments.
Divide the square into four outer corners and the central diamond; identify the triangles formed by dividing the corner segments.
Analyze the corner regions
Observe the four corners of the square. Each corner has a smaller triangle formed by the intersection of the diagonal lines. There are 4 small triangles in the four corners.
Analyze the remaining regions
The large central square (diamond shape) is divided into 4 triangles by its own diagonals. Counting the 4 small corner triangles plus the 4 triangles inside the central diamond gives 4 + 4 = 8.
A: 6 is incorrect as it misses the total count of 8. B: 7 is incorrect as it fails to account for all distinct triangle shapes. D: 9 is incorrect as it overcounts by including non-existent regions.
C is correct because there are 4 small triangles at the corners and 4 triangles formed within the central diamond, totaling 8 triangles.
When counting figures, always label components systematically or use symmetry to avoid double-counting overlapping areas.
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