Both diagonals of a square are drawn, and the middle of the top side is joined to both bottom corners. Count all the triangles.

With a vertex at the top midpoint M: the two slanting lines from M with the base or a diagonal, 3; the top edge with each slanting line, 3 + 3; that is 9. The diagonals alone: 4 quarters and 4 halves, 8. The rest: two small ones beside the centre, two along the left and right sides, two standing on the base, 6. Total $9+8+6=23$.