Unit 2: Investigation 1 - Connecticut Core Standards
... of which will require a reflection. Following the discussion above and the student activity, ask the class to draw conclusions about conditions for two segments or two angles to be congruent. They should arrive at the following: If two segments have the same length, then they are congruent. If two a ...
... of which will require a reflection. Following the discussion above and the student activity, ask the class to draw conclusions about conditions for two segments or two angles to be congruent. They should arrive at the following: If two segments have the same length, then they are congruent. If two a ...
5. Circles and lines 5.1. Circles. A circle Σ is the set of points at fixed
... 5. Circles and lines 5.1. Circles. A circle Σ is the set of points at fixed distance r > 0 from a given point, its center. The distance r is called the radius of the circle Σ. The circle Σ divides the plane into two regions: the inside, which is the set of points at distance less than r from the cen ...
... 5. Circles and lines 5.1. Circles. A circle Σ is the set of points at fixed distance r > 0 from a given point, its center. The distance r is called the radius of the circle Σ. The circle Σ divides the plane into two regions: the inside, which is the set of points at distance less than r from the cen ...
Scope Informal Geo FINAL - The School District of Palm Beach County
... • Identify corresponding parts of congruent triangles • Use the SSS and SAS tests for congruence • Use the ASA and AAS tests for congruence • Identify and construct medians in triangles • Identify and construct altitudes and perpendicular bisectors in triangles • Identify and use angle bisectors in ...
... • Identify corresponding parts of congruent triangles • Use the SSS and SAS tests for congruence • Use the ASA and AAS tests for congruence • Identify and construct medians in triangles • Identify and construct altitudes and perpendicular bisectors in triangles • Identify and use angle bisectors in ...
Chapter 1
... 1. Draw a circle with center X 2. Draw Point Y on the bottom of your circle 3. Create line ZY tangent to the circle at Point Y 4. Draw the radius to the point of tangency and measure the angle formed by the tangent and the radius (L XYZ) ...
... 1. Draw a circle with center X 2. Draw Point Y on the bottom of your circle 3. Create line ZY tangent to the circle at Point Y 4. Draw the radius to the point of tangency and measure the angle formed by the tangent and the radius (L XYZ) ...
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.