Chapter 8 Right Triangles and Trigonometry
... software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). 3. Given a rectangle, parallelogram, trapezoid, or re ...
... software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). 3. Given a rectangle, parallelogram, trapezoid, or re ...
Geometry Regents Curriculum Guide
... 1. identify perpendicular lines 2. identify perpendicular planes 3. define line, segment and ray 4. define a plane and what the minimum requirements are for a plane (3 points) 5. know the differences in what is formed when lines intersect lines, planes intersect planes, and lines intersect planes. 6 ...
... 1. identify perpendicular lines 2. identify perpendicular planes 3. define line, segment and ray 4. define a plane and what the minimum requirements are for a plane (3 points) 5. know the differences in what is formed when lines intersect lines, planes intersect planes, and lines intersect planes. 6 ...
Manassas City Public Schools (4-19-07)
... Non-congruent figures may have the same shape but not the same size. The symbol for congruency is “”. Sides are congruent if they have the same length. Angles have congruency if they have the same measure or number of degrees. The determination of the congruence or noncongruence of two fi ...
... Non-congruent figures may have the same shape but not the same size. The symbol for congruency is “”. Sides are congruent if they have the same length. Angles have congruency if they have the same measure or number of degrees. The determination of the congruence or noncongruence of two fi ...
polypro P1
... of the regular pentagon are 108°, so we can fit only three together at a vertex, giving us the dodecahedron. ...
... of the regular pentagon are 108°, so we can fit only three together at a vertex, giving us the dodecahedron. ...
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ.Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis.Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups: Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan angles are also called Cardan angles; nautical angles; heading, elevation, and bank; or yaw, pitch, and roll. Sometimes, both kinds of sequences are called ""Euler angles"". In that case, the sequences of the first group are called proper or classic Euler angles.