Find the number of triangles in the given figure.

Concept: To count every triangle in a compound figure built from several intersecting lines, first identify all the smallest (undivided) triangular regions the lines cut out, then build every larger triangle as a union of 2, 3, or 4 of these regions. A combination is a valid triangle only when its complete outer boundary runs along straight, unbroken lines that are actually drawn in the figure.

Label the ten points of the figure as shown.

Counting region by region:

1. Single-region (simplest) triangles — 12 in total: ABG, BGI, BCI, CHI, GHI, CDH, DEH, GHJ, EHJ, EFJ, FGJ, AFG.

2. Two-region triangles — 10 in total: ABF, CDE, BCG, BCH, BGH, CGH, FGH, EGH, EFH, EFG.

3. Three-region triangles — 4 in total: ABH, AFH, CDG, DEG.

4. Four-region triangles — 2 in total: BFH, CEG.

5. Total number of triangles = 12 + 10 + 4 + 2 = 28.

Cross-check: the figure has a left-right mirror symmetry (A↔D, B↔C, F↔E, G↔H, with I and J each mapping to itself) and a top-bottom mirror symmetry (B↔F, C↔E, I↔J, with A, D, G, H each mapping to itself). Every triangle in each group above pairs up with a matching mirror-image triangle also in that same group — an independent check that none was missed, double-counted, or misclassified.