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What is a Euclidean triangle?

Updated: 4/28/2022
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12y ago

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180 degrees

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12y ago
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Q: What is a Euclidean triangle?
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Can a triangle be coplanar?

In Euclidean plane geometry every triangle MUST BE coplanar.


Can an obtuse angled triangle be an equilateral triangle?

No way. Never. At least not in Euclidean geometry.


What is the sum of the angles in a euclidean triangle?

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No, not in plane (Euclidean) geometry.


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In normal geometry, it's not possible to make a triangle with two obtuse angles. It is possible to make a triangle with two obtuse angles in spherical geometry -- it's a kind of "spherical triangle". It is possible to make a triangle with two obtuse angles in some kinds of non-Euclidean geometry -- it's a kind of "non-Euclidean triangle".


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Any number you like.


What is the sumof the measure of the three anglesin a triangle?

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In Euclidean geometry a right angle triangle has two acute angles. All others have three.


Is it true that an obtuse triangle can have a right angle?

In Euclidean geometry, a triangle must be one of these: acute, obtuse, or right. Maybe there is a non-Euclideangeometry for which some obtuse triangles can contain a right angle, but it doesn't happen in Euclidean geometry.


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No. A triangle's angles must add up to 180 degrees so it cannot have two right angles. However, the answer is yes if you are talking about a triangle on the surface of a sphere. In this case the geometry is non-Euclidean. If you are staying with standard Euclidean geometry, then the answer no above is correct.