Geometry - Chapter 1 Day #1 - Somerset Independent Schools
... What is the converse of the following statement? "If a whole number has a as its last digit, then the number is evenly divisible by 10./1 a. If a number is evenly divisible by la, then it is a whole number. b. If a whole number is divisible by la, then it is an even number. c. If a whole number is e ...
... What is the converse of the following statement? "If a whole number has a as its last digit, then the number is evenly divisible by 10./1 a. If a number is evenly divisible by la, then it is a whole number. b. If a whole number is divisible by la, then it is an even number. c. If a whole number is e ...
5-6 Inequalities in One Triangle
... Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle. ...
... Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle. ...
10-3 practice worksheet
... Find the area of each regular polygon with the given radius or apothem. If your answer is not an integer, leave it in simplest radical form. ...
... Find the area of each regular polygon with the given radius or apothem. If your answer is not an integer, leave it in simplest radical form. ...
Unit-1: An Informal Introduction to Geometry
... a.A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b.The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 2. Given two figures, use the definition of similarity in ...
... a.A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b.The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 2. Given two figures, use the definition of similarity in ...
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.