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  2. Acute and obtuse triangles - Wikipedia

    en.wikipedia.org/wiki/Acute_and_obtuse_triangles

    If angle C is obtuse then for sides a, b, and c we have [4]: p.1, #74 < + <, with the left inequality approaching equality in the limit only as the apex angle of an isosceles triangle approaches 180°, and with the right inequality approaching equality only as the obtuse angle approaches 90°.

  3. Rhombohedron - Wikipedia

    en.wikipedia.org/wiki/Rhombohedron

    A rhombohedron has two opposite apices at which all face angles are equal; a prolate rhombohedron has this common angle acute, and an oblate rhombohedron has an obtuse angle at these vertices. A cube is a special case of a rhombohedron with all sides square.

  4. Lambert quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Lambert_quadrilateral

    In geometry, a Lambert quadrilateral (also known as Ibn al-Haytham–Lambert quadrilateral), [1] [2] is a quadrilateral in which three of its angles are right angles. Historically, the fourth angle of a Lambert quadrilateral was of considerable interest since if it could be shown to be a right angle, then the Euclidean parallel postulate could ...

  5. Isosceles triangle - Wikipedia

    en.wikipedia.org/wiki/Isosceles_triangle

    Whether an isosceles triangle is acute, right or obtuse depends only on the angle at its apex. In Euclidean geometry, the base angles can not be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle. [9]

  6. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry is Euclidean and obtuse angles if the geometry is elliptic. The sum of the measures of the angles of any triangle is less than 180° if the geometry is hyperbolic, equal to 180° if the geometry is Euclidean, and greater than 180 ...

  7. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    An acute trapezoid has two adjacent acute angles on its longer base edge. An obtuse trapezoid on the other hand has one acute and one obtuse angle on each base. An isosceles trapezoid is a trapezoid where the base angles have the same measure. As a consequence the two legs are also of equal length and it has reflection symmetry. This is ...

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  9. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. [12] An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [11] ("obtuse" meaning "blunt"). An angle equal to ⁠ 1 / 2 ⁠ turn (180° or π radians) is called a straight angle. [10]