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  2. Right angle - Wikipedia

    en.wikipedia.org/wiki/Right_angle

    The straight lines which form right angles are called perpendicular. [8] Euclid uses right angles in definitions 11 and 12 to define acute angles (those smaller than a right angle) and obtuse angles (those greater than a right angle). [9] Two angles are called complementary if their sum is a right angle. [10]

  3. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    Angles whose sum is a right angle are called complementary. Complementary angles are formed when a ray shares the same vertex and is pointed in a direction that is in between the two original rays that form the right angle. The number of rays in between the two original rays is infinite. Angles whose sum is a straight angle are supplementary ...

  4. Angle trisection - Wikipedia

    en.wikipedia.org/wiki/Angle_trisection

    The triple-angle formula gives an expression relating the cosines of the original angle and its trisection: cos θ = 4 cos 3 ⁠ θ / 3 ⁠ − 3 cos ⁠ θ / 3 ⁠. It follows that, given a segment that is defined to have unit length, the problem of angle trisection is equivalent to constructing a segment whose length is the root of a cubic ...

  5. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin β = 0.5, the angle β can equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the cosine value unambiguously determines its angle.

  6. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

  7. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    An angle equal to ⁠ 1 / 4 ⁠ turn (90° or ⁠ π / 2 ⁠ radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. [7] An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [6] ("obtuse" meaning "blunt").

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