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Label the intersections to systematically count individual, combined, and composite triangles while ensuring no overlapping figure is missed.
Label the intersections to systematically count individual, combined, and composite triangles while ensuring no overlapping figure is missed.
Categorize by size
Label the central point 'O' and the vertices. 1. There are 4 small triangles directly around the central point. 2. There are 2 triangles formed by combining two smaller segments. 3. There are 3 larger triangles forming the main outer partitions.
Systematic Counting
Counting method: Identify 4 triangles touching the central point (O), 2 triangles involving segments from the corners, and 3 larger triangles formed by the primary dividing lines crossing the square, summing to a total of 9 distinct triangles.
A: 10 exceeds the total number of distinct triangles found; C: 8 misses one of the composite triangle configurations; D: 7 misses two of the valid composite triangle configurations.
B is correct because a rigorous manual count of all small, medium, and composite triangles within the provided geometry confirms a total of 9 triangles.
When counting triangles in a complex figure, always trace the boundaries of each triangle one by one starting from the smallest to the largest to avoid double-counting.
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