Can a right triangle can be an equilateral triangle? - Answers

Short Answer: no Long Answer: Most people consider Euclidean Geometry when taking about standard shapes such as triangles and squares. In Euclidean Geometry: all equilateral triangles have angles of 60°. Therefore an equilateral triangle doesn't have a right angle. However, in Non-Euclidean Geometry (Elliptic Geometry) a triangle can have all angles at 90°. Consider going for a walk at the North Pole. Start going South (all directions are South), then turn at a right angle (90°) to go East, then turn again at a right angle (90°) to go North and you would end up at your starting point (assuming the distance travelled in each direction is the same). The 'triangle' you made would have 3 right angles!!