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  2. Similarity (geometry) - Wikipedia

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

    Any two pairs of angles are congruent, [4] which in Euclidean geometry implies that all three angles are congruent: [a] If ∠BAC is equal in measure to ∠B'A'C', and ∠ABC is equal in measure to ∠A'B'C', then this implies that ∠ACB is equal in measure to ∠A'C'B' and the triangles are similar. All the corresponding sides are ...

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  4. Right angle - Wikipedia

    en.wikipedia.org/wiki/Right_angle

    In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or ⁠ / 2 ⁠ radians [1] corresponding to a quarter turn. [2] If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. [ 3 ]

  5. Kite (geometry) - Wikipedia

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

    Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [1] but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. [2] [3] A kite may also be called a dart, [4] particularly if it is ...

  6. Right kite - Wikipedia

    en.wikipedia.org/wiki/Right_kite

    In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. [1] That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right ...

  7. Parallel postulate - Wikipedia

    en.wikipedia.org/wiki/Parallel_postulate

    In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (Pythagoras' theorem). [6] [7] The law of cosines, a generalization of Pythagoras' theorem. There is no upper limit to the area of a triangle. (Wallis axiom) [8] The summit angles of the Saccheri quadrilateral are 90°.

  8. Range of a projectile - Wikipedia

    en.wikipedia.org/wiki/Range_of_a_projectile

    The horizontal ranges of a projectile are equal for two complementary angles of projection with the same velocity. The following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight .

  9. Gimbal lock - Wikipedia

    en.wikipedia.org/wiki/Gimbal_lock

    It is possible to imagine an airplane rotated by the above-mentioned Euler angles using the X-Y-Z convention. In this case, the first angle - is the pitch. Yaw is then set to and the final rotation - by - is again the airplane's pitch. Because of gimbal lock, it has lost one of the degrees of freedom - in this case the ability to roll.

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