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In non-Euclidean geometry triangles on a sphere have 180 degrees?
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In non-Euclidean geometry triangles on a sphere have exactly 180 degrees?
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Can a triangle have two right angels?
In normal (Euclidean) geometry, no. However, there are some cases where a triangle can be drawn which does have two right angles.Imagine drawing a great triangle on the earth between three points. The first point is on the equator in Brazil, the second point is at the north pole, and the third point is on the equator in Africa. The two angles drawn from the equator to the north pole are both 90 degrees.This is because the surface of a sphere is not flat, but curved, and it allows the angles of triangles to add up to almost 360 degrees. We call this non-euclidean geometry.
Does a right triangle have three right angles?
Not in traditional, 2 dimensional, euclidean geometry, because a triangles angles always equal 180º .However, there is a branch of Geometry that deals with a coordinate system on a sphere, instead of a plane, and in spherical geometry a triangle with three right angles is very much possible. Consider, for example, the triangle bounded by the Prime Meridian, 90o west longitude, and the equator.
Curved line in geometry?
In plane, or Euclidean geometry, a line usually means a straight line and a cure often refers to something else. A semicircle would be a curved line for example. But, imagine, and it should not be hard since it is reality, that we DO NOT live on a flat surface. We live on something more like a sphere. The lines are now defined as great circles. Great circles are line that run along the surface of the sphere and cut it into two parts. Imagine a plane that goes through the center of the sphere and cuts it in half. The intersection of the plane and the sphere is a great circle. These lines are not the straight lines we saw in plane of Euclidean geometry. One big difference is that any two or more will intersect. In other geometries, one called hyperbolic geometry, the lines are either traditional vertical lines or semicircles that intersect the x axis. So what I am trying to say is that curved lines depends on the geometry you are talking about and there are many of them. In Euclidean geometry we define a line as a straight curve. So the idea of a curve is more general and a line is a specific case. It has no height or width.
