rhombuses, kites and trapezia
... A rectangle is a parallelogram, so it has rotationsymmetry of order 2 about the intersection of its diagonals. This is even clearer in a rectangle than in a general parallelogram because the diagonals have equal length, so their intersection is the circumcentre of the circumcircle passing through al ...
... A rectangle is a parallelogram, so it has rotationsymmetry of order 2 about the intersection of its diagonals. This is even clearer in a rectangle than in a general parallelogram because the diagonals have equal length, so their intersection is the circumcentre of the circumcircle passing through al ...
PowerPoint Presentation - 12.215 Modern Navigation
... co-latitudes of the other two points • Angles: When one of the points is the North pole, the angles at the other two points are the azimuth or bearing to the other point. ...
... co-latitudes of the other two points • Angles: When one of the points is the North pole, the angles at the other two points are the azimuth or bearing to the other point. ...
Geometry_How much do I know - Homepage | Talk Maths Talk
... Some shapes are composite shapes, which need to be split up into their basic elements (rectangles/triangles). There is often more than one way to do this. In the example above, we have a rectangle and a triangle. We can either use the triangle area formula directly to find the area of the shaded tri ...
... Some shapes are composite shapes, which need to be split up into their basic elements (rectangles/triangles). There is often more than one way to do this. In the example above, we have a rectangle and a triangle. We can either use the triangle area formula directly to find the area of the shaded tri ...
Theorem
... All three of these inscribed angles intercept arc AB. Theorem : An inscribed angle is equal to half of its intercepted arc. ...
... All three of these inscribed angles intercept arc AB. Theorem : An inscribed angle is equal to half of its intercepted arc. ...
A B C D - mendeleev08-09
... each other, then it is a parallelogram. • Both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. • In a quadrilateral, if any two consecutive angles are supplementary, then it is a parallelogram. ...
... each other, then it is a parallelogram. • Both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. • In a quadrilateral, if any two consecutive angles are supplementary, then it is a parallelogram. ...
Geometry Honors
... triangles congruent by SAS? a. T S b. D S c. S L d. D G 3. Suppose TD=10 cm, DM=9cm, TM=11 cm, SL=11 cm, and SG=9 cm. What else do you need to know in order to prove that the two triangles are congruent by SSS? a. LG= 9cm b. TD=SL c. GL= 10 cm d. TM=SG ...
... triangles congruent by SAS? a. T S b. D S c. S L d. D G 3. Suppose TD=10 cm, DM=9cm, TM=11 cm, SL=11 cm, and SG=9 cm. What else do you need to know in order to prove that the two triangles are congruent by SSS? a. LG= 9cm b. TD=SL c. GL= 10 cm d. TM=SG ...
Measuring in the Round
... wheels of a moving car, or the seats on a Ferris wheel. These periodic or repetitive situations can be mathematically modeled using trigonometric functions, which is why the unit circle is the foundation of this investigation. I. Circular Motion and Degree Measure Consider the angles that can be mod ...
... wheels of a moving car, or the seats on a Ferris wheel. These periodic or repetitive situations can be mathematically modeled using trigonometric functions, which is why the unit circle is the foundation of this investigation. I. Circular Motion and Degree Measure Consider the angles that can be mod ...
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.