How many triangles are there in the given figure?
10
The figure is a closed quadrilateral in which extra straight segments (diagonals) are drawn from the vertices, so many triangles overlap one another.
Whenever triangles overlap like this, the safe method is to count in an order: first the smallest single triangles, then triangles made by joining two small parts, and finally the largest triangles formed by the outer lines.
Smallest triangles: counting each individual triangular region created by the intersecting lines gives 6 basic triangles.
Composite triangles of two parts: joining two adjacent smallest triangles along a common line forms 3 more triangles.
Largest triangles: the outer boundary segments combine three regions together to form 1 more large triangle.
Adding every category: \(6 + 3 + 1 = 10\).
No triangle is counted twice and none is missed, so the total stays 10.
Hence the given figure contains 10 triangles.
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