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The triangles in both spaces have properties different from the triangles in Euclidean space. For example, as mentioned above, the internal angles of a triangle in Euclidean space always add up to 180°. However, the sum of the internal angles of a hyperbolic triangle is less than 180°, and for any spherical triangle, the sum is more than 180 ...
In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...
Triangle – 3 sides Acute triangle; Equilateral triangle; Heptagonal triangle; Isosceles triangle. Golden Triangle; Obtuse triangle; Rational triangle; Heronian triangle. Pythagorean triangle; Isosceles heronian triangle; Primitive Heronian triangle; Right triangle. 30-60-90 triangle; Isosceles right triangle; Kepler triangle; Scalene triangle ...
Hyperbolic triangles have some properties that are the opposite of the properties of triangles in spherical or elliptic geometry: The angle sum of a triangle is less than 180°. The area of a triangle is proportional to the deficit of its angle sum from 180°. Hyperbolic triangles also have some properties that are not found in other geometries:
Many results about plane figures are proved, for example, "In any triangle, two angles taken together in any manner are less than two right angles." (Book I proposition 17) and the Pythagorean theorem "In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle."
An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse ...
In Euclidean geometry, an angle is the figure ... the two acute angles in a right triangle are complementary because the ... For example, an angle of 30 degrees is ...
In Euclidean geometry, the triangle postulate states that the sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate. [1] In the presence of the other axioms of Euclidean geometry, the following statements are equivalent: [2] Triangle postulate: The sum of the angles of a triangle is two ...
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