Geometry – Lines and Angles Two lines are parallel in a plane (2
... Two lines are perpendicular in a plane if they cross in 90o angles.
Two angles are complementary if their measures add to be 90o.
Two angles are supplementary if their measures add to be 180o.
Congruent: coinciding exactly when superimposed. (American Heritage Dictionary, 4th
ed.)
Acute Angle: An an ...
Plane of rotation
In geometry, a plane of rotation is an abstract object used to describe or visualise rotations in space. In three dimensions it is an alternative to the axis of rotation, but unlike the axis of rotation it can be used in other dimensions, such as two, four or more dimensions.Mathematically such planes can be described in a number of ways. They can be described in terms of planes and angles of rotation. They can be associated with bivectors from geometric algebra. They are related to the eigenvalues and eigenvectors of a rotation matrix. And in particular dimensions they are related to other algebraic and geometric properties, which can then be generalised to other dimensions.Planes of rotation are not used much in two and three dimensions, as in two dimensions there is only one plane so identifying the plane of rotation is trivial and rarely done, while in three dimensions the axis of rotation serves the same purpose and is the more established approach. The main use for them is in describing more complex rotations in higher dimensions, where they can be used to break down the rotations into simpler parts. This can be done using geometric algebra, with the planes of rotations associated with simple bivectors in the algebra.