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2. Solution of triangles - Wikipedia

   en.wikipedia.org/wiki/Solution_of_triangles

   Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique. If b < c, the angle γ may be acute: γ = arcsin D or obtuse: γ ′ = 180° − γ. The figure on right shows the point C, the side b and the angle γ as the first solution, and the point C ′, side b ′ and the angle γ ′ as the ...

3. Hilbert's axioms - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_axioms

   Let an angle ∠ (h,k) be given in the plane α and let a line a′ be given in a plane α′. Suppose also that, in the plane α′, a definite side of the straight line a′ be assigned. Denote by h′ a ray of the straight line a′ emanating from a point O′ of this line.

4. Lambert quadrilateral - Wikipedia

   en.wikipedia.org/wiki/Lambert_quadrilateral

   In hyperbolic geometry the fourth angle is acute, in Euclidean geometry it is a right angle and in elliptic geometry it is an obtuse angle. A Lambert quadrilateral can be constructed from a Saccheri quadrilateral by joining the midpoints of the base and summit of the Saccheri quadrilateral. This line segment is perpendicular to both the base ...

5. Parallel postulate - Wikipedia

   en.wikipedia.org/wiki/Parallel_postulate

   If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:

6. Three-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Three-dimensional_space

   In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space.

7. Foundations of geometry - Wikipedia

   en.wikipedia.org/wiki/Foundations_of_geometry

   A typical result is the 1:3 ratio between the volume of a cone and a cylinder with the same height and base. The parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

8. Base (geometry) - Wikipedia

   en.wikipedia.org/wiki/Base_(geometry)

   In a triangle, any arbitrary side can be considered the base. The two endpoints of the base are called base vertices and the corresponding angles are called base angles. The third vertex opposite the base is called the apex. The extended base of a triangle (a particular case of an extended side) is the line that contains the base.

9. Acute and obtuse triangles - Wikipedia

   en.wikipedia.org/wiki/Acute_and_obtuse_triangles

   The equilateral triangle, with three 60° angles, is acute. The Morley triangle, formed from any triangle by the intersections of its adjacent angle trisectors, is equilateral and hence acute. The golden triangle is the isosceles triangle in which the ratio of the duplicated side to the base side equals the golden ratio. It is acute, with ...