Simple glue and nails (or a brad nailer) are often sufficient for decorative pieces. For structural stability, consider using splines or dados to increase the surface area for the wood glue.
For an equilateral triangle, each piece should be cut at a 30-degree angle (to create 60-degree internal angles). For a right-angle frame, a 45-degree miter is standard. Taniarar
Where medians meet; the geometric center of the triangle. Simple glue and nails (or a brad nailer)
Where angular bisectors meet; the center of an inscribed circle. Taniarar
Sides of 2 ft, 2 ft, and 7 ft cannot form a triangle because is less than 7. Woodworking Assembly
Watch this brief explanation of why some rearranged triangular puzzles seem to have a missing piece due to slight slope differences:
