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  2. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical and hence are equal.

  3. Transversal (geometry) - Wikipedia

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

    Corresponding angles are the four pairs of angles that: have distinct vertex points, lie on the same side of the transversal and; one angle is interior and the other is exterior. Two lines are parallel if and only if the two angles of any pair of corresponding angles of any transversal are congruent (equal in measure).

  4. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    Angles ∠ ADB and ∠ ADC form a linear pair, that is, they are adjacent supplementary angles. Since supplementary angles have equal sines, Since supplementary angles have equal sines, sin ⁡ ∠ A D B = sin ⁡ ∠ A D C . {\displaystyle {\sin \angle ADB}={\sin \angle ADC}.}

  5. Angles between flats - Wikipedia

    en.wikipedia.org/wiki/Angles_between_flats

    To construct a pair of subspaces with any given set of angles , …, in a (or larger) dimensional Euclidean space, take a subspace with an orthonormal basis (, …,) and complete it to an orthonormal basis (, …,) of the Euclidean space, where .

  6. Molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Molecular_geometry

    A bond angle is the geometric angle between two adjacent bonds. Some common shapes of simple molecules include: Linear: In a linear model, atoms are connected in a straight line. The bond angles are set at 180°. For example, carbon dioxide and nitric oxide have a linear molecular shape.

  7. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    The pair of ⁡, ⁡) is the ... Both sine and cosine functions with multiple angles may appear as their linear combination, resulting in a polynomial.

  8. Parallel (geometry) - Wikipedia

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

    The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.

  9. Euclidean plane - Wikipedia

    en.wikipedia.org/wiki/Euclidean_plane

    In the technical language of linear algebra, the plane is two-dimensional because every point in the plane can be described by a linear combination of two independent vectors. Dot product, angle, and length

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