Geometry Unit 10 Plan (July 2015)
... Instruction should include constructions related to HSG-CO.D.13 and learning target 6 for constructing an equilateral triangle, a square, and a regular hexagon inscribed in a circle. The first part of HSG-C.A.3 is included in Unit 5 instruction but not assessed on the common assessment. Identifying ...
... Instruction should include constructions related to HSG-CO.D.13 and learning target 6 for constructing an equilateral triangle, a square, and a regular hexagon inscribed in a circle. The first part of HSG-C.A.3 is included in Unit 5 instruction but not assessed on the common assessment. Identifying ...
Arrange these statements into two columns, so that the statements in
... facts. The second part consists of mathematical arguments deducing the deductions from the facts. In framing these arguments, you can use other deductions you have already proved, as long as ultimately everything leads back to the facts. You reference by number each statement that is needed in makin ...
... facts. The second part consists of mathematical arguments deducing the deductions from the facts. In framing these arguments, you can use other deductions you have already proved, as long as ultimately everything leads back to the facts. You reference by number each statement that is needed in makin ...
In geometry, angles are measured in units called . The symbol is
... Example 3: Use a protractor to draw an angle having each measurement. Then classify each angle. a) 115 ...
... Example 3: Use a protractor to draw an angle having each measurement. Then classify each angle. a) 115 ...
Volumes, Perimeters, Circles, Spheres, Triangles, Angles, Rays and
... If one of the angles meets at 90°, it is called a right triangle. The other two angles then sum to 90° as well, and are called complementary. Equivalently, the sum of two complementary angles is 90°. If the lengths a and b are given for the two legs of a right triangle, the hypotenuse c is found by ...
... If one of the angles meets at 90°, it is called a right triangle. The other two angles then sum to 90° as well, and are called complementary. Equivalently, the sum of two complementary angles is 90°. If the lengths a and b are given for the two legs of a right triangle, the hypotenuse c is found by ...
0002_hsm11gmtr_0301.indd
... In Exercises 4–7, use the diagram to name each of the following. 4. a line that is parallel to 5. a line that is skew to 6. a plane that is parallel to NRTP 7. three lines that are parallel to ...
... In Exercises 4–7, use the diagram to name each of the following. 4. a line that is parallel to 5. a line that is skew to 6. a plane that is parallel to NRTP 7. three lines that are parallel to ...
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.