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A heptagonal triangle is an obtuse scalene triangle whose vertices coincide with the first, second, and fourth vertices of a regular heptagon. Thus its sides coincide with one side and the adjacent shorter and longer diagonals of the regular heptagon. All heptagonal triangles are similar , and so they are collectively known as the heptagonal triangle. Its angles have measures π / 7 , 2 π / 7 , {\displaystyle \pi /7,2\pi /7,} and 4 π / 7 , {\displaystyle 4\pi /7,} and it is the only triangle with angles in the ratios 1:2:4. The heptagonal triangle has various remarkable properties.
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