1. **Stating the problem:** We need to find how many triangles are in the given geometric figure, which is a large triangle subdivided by three segments connecting vertices to points inside, creating smaller triangles. 2. **Understanding the figure:** The large triangle is divided by three segments intersecting inside, forming smaller triangles. Each segment connects a vertex to a point on the opposite side or inside the triangle. 3. **Counting triangles:** - There are 3 small triangles formed at each corner by the segments. - There are 3 medium triangles formed between these small triangles. - There is 1 large triangle (the original one). - Additionally, 5 other triangles are formed by combinations of these segments and intersections. 4. **Summing all triangles:** $$3 + 3 + 1 + 5 = 12$$ 5. **Final answer:** The total number of triangles in the figure is **12**.