Chapter 6 Proportions and Similarity
... into segments of proportional length Tri. Proportion Thm. Converse – If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side ...
... into segments of proportional length Tri. Proportion Thm. Converse – If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side ...
Q3 - FCCSC
... 1. Verify experimentally the properties of dilations given by a center and a scale factor: 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 t ...
... 1. Verify experimentally the properties of dilations given by a center and a scale factor: 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 t ...
Practice A3
... At each vertex of a triangle, the angle formed by one side and an extension of the other side is called an exterior angle of the triangle. For each exterior angle of a triangle, the remote interior angles are the interior angles that are not adjacent to that exterior angle. In the diagram below, ∠B ...
... At each vertex of a triangle, the angle formed by one side and an extension of the other side is called an exterior angle of the triangle. For each exterior angle of a triangle, the remote interior angles are the interior angles that are not adjacent to that exterior angle. In the diagram below, ∠B ...
Secondary II - Northern Utah Curriculum Consortium
... same locations in both intersections. Top left and top left, bottom right and bottom right, etc. Alternate interior angles: A pair of angles formed by a pair of lines and a transversal that are both on the interior of the pair of lines, but on opposite sides of the transversal. Alternate exterior an ...
... same locations in both intersections. Top left and top left, bottom right and bottom right, etc. Alternate interior angles: A pair of angles formed by a pair of lines and a transversal that are both on the interior of the pair of lines, but on opposite sides of the transversal. Alternate exterior an ...
Solving Right Triangles
... measures of all three angles when only some of these quantities are given. The right triangle description of a trigonometric function relates three quantities: the angle and two sides of the right triangle. When two of these three quantities are known, then the third can always be found. Example: ...
... measures of all three angles when only some of these quantities are given. The right triangle description of a trigonometric function relates three quantities: the angle and two sides of the right triangle. When two of these three quantities are known, then the third can always be found. Example: ...
Try Your Hand at Drawing Triangles
... Try Your Hand at Drawing Triangles 1 point In this activity, you will draw six triangles: an isosceles triangle, an equilateral triangle, a scalene triangle, a right triangle, and acute triangle, and an obtuse triangle. *You are to: 1). name each triangle 2). label the measurements of ALL of its sid ...
... Try Your Hand at Drawing Triangles 1 point In this activity, you will draw six triangles: an isosceles triangle, an equilateral triangle, a scalene triangle, a right triangle, and acute triangle, and an obtuse triangle. *You are to: 1). name each triangle 2). label the measurements of ALL of its sid ...
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.