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How many degrees would a triangle have in hyperbolic geometry?
170 degrees
Rotating a triangle by 50 will change the measures of the exterior angles by?
Rotating a triangle by 50 degrees will not change the measures of its exterior angles. Exterior angles are defined based on the triangle's geometry and the positions of its vertices, which remain unchanged by rotation. Thus, regardless of the triangle's orientation, the exterior angles will retain their original measures.
Is the sum of the measures of the angles of a triangle always 180?
Yes - in the case of triangles in Euclidian geometry. That is, basically triangles in a plane.
Did Lobachevsky negation created spherical geometry?
Lobachevsky's work did not create spherical geometry; rather, he is known for developing hyperbolic geometry, which deviates from Euclidean principles. Spherical geometry, on the other hand, is based on the properties of figures on the surface of a sphere and includes concepts such as great circles and the sum of angles in a triangle exceeding 180 degrees. Both geometries are non-Euclidean, but they arise from different fundamental assumptions about space. Lobachevsky's contributions helped to expand the understanding of non-Euclidean geometries, including both hyperbolic and spherical forms.
What if the angles of a triangle don't add up to 180 degrees?
If the sum is not 180° you are not in Euclidean space.If the three angles of a triangle add up to more than 180° then you are in a spherical geometry, if the sum is less than 180° it is a hyperbolic space.It must add up to 180 degrees. If not, then it either isn't a triangle, or it is a triangle on some non-planar surface (e.g. a triangle formed by taking three points on a globe).
How many degrees would a triangle have in hyperbolic geometry?
170 degrees
In hyperbolic geometry a triangle could potentially have how many degrees?
170
Can a triangle can have two parellel sides?
A Plane triangle cannot have parallel sides. A triangle on a sphere, represented in Mercator projection may do so, but that still does not make it so, for that is in spherical geometry. And there are other geometries than Euclidean (plane). Hyperbolic Geometry and Elliptic Geometry are the names of another two. These geometries are consistent within themselves, but some of the theorems in Euclidean geometry have different answers in these alternate geometries.
which is the inverse of the following conditionalAll scalene triangles have three angles with distinct measures.?
If a triangle is not scalene, then the triangle does not have three angles with distinct measures.
Rotating a triangle by 50 will change the measures of the exterior angles by?
Rotating a triangle by 50 degrees will not change the measures of its exterior angles. Exterior angles are defined based on the triangle's geometry and the positions of its vertices, which remain unchanged by rotation. Thus, regardless of the triangle's orientation, the exterior angles will retain their original measures.
Which of the following could be the side measures of a right triangle?
There are no numbers on that list that could be the sides of a right triangle. Oh, all right. The following is the answer:
Is the sum of the measures of the angles of a triangle always 180?
Yes - in the case of triangles in Euclidian geometry. That is, basically triangles in a plane.
What is right triangle geometry?
A right triangle in geometry is a triangle that has 90 degrees as one of its angles.
Prove that the sum of angles of a triangle is equal to 180 degress?
The proof is pretty simple, but hard to see without the pictures. SO here is a link to the proof with some pics. http://www.apronus.com/geometry/triangle.htm The answer depends on your geometry: In Euclidean geometry, the angle sum is 180 degrees, in Hyperbolic geometry it is less than 180 degrees, and in Elliptical geometry it is greater than 180 degrees.
which figure is a counterexample to the following conditional statementIf a triangle has an angle that measures 60°, then it is equilateral.?
A+
Where does the altitude of a triangle intersect geometry?
The altitude of a triangle IS a geometric concept so it intersects geometry in its very existence.
What if the angles of a triangle don't add up to 180 degrees?
If the sum is not 180° you are not in Euclidean space.If the three angles of a triangle add up to more than 180° then you are in a spherical geometry, if the sum is less than 180° it is a hyperbolic space.It must add up to 180 degrees. If not, then it either isn't a triangle, or it is a triangle on some non-planar surface (e.g. a triangle formed by taking three points on a globe).
