Curriculum Guide
... polygons according to the number of sides and angles. Name sets of polygons e.g. the set of triangles, quadrilaterals, pentagons and hexagons. Record the properties of these polygons on a given table. Draw different triangles, quadrilaterals, pentagons and hexagons. Identify right angles. Use cardbo ...
... polygons according to the number of sides and angles. Name sets of polygons e.g. the set of triangles, quadrilaterals, pentagons and hexagons. Record the properties of these polygons on a given table. Draw different triangles, quadrilaterals, pentagons and hexagons. Identify right angles. Use cardbo ...
Investigation
... Polygons can be classified as concave and convex. Convex Polygon: A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note t ...
... Polygons can be classified as concave and convex. Convex Polygon: A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note t ...
Geometry Proofs Reference Sheet
... divides an angle into TWO equal parts.” #33. Angle Bisector Theorem – says that “If a segment, ray, line or plane is an angle bisector, then it divides an angle so that each part of the angle is equal to ONE HALF of the whole angle.” It also says: “If a point is on the bisector of an angle, then the ...
... divides an angle into TWO equal parts.” #33. Angle Bisector Theorem – says that “If a segment, ray, line or plane is an angle bisector, then it divides an angle so that each part of the angle is equal to ONE HALF of the whole angle.” It also says: “If a point is on the bisector of an angle, then the ...
Informal Proof – Angle Dissection
... An informal proof that is often used is the process of having our students create a triangle on a piece of paper, naming the three angles A, B, and C. Cut out the triangle and then draw a line on a piece of paper and then lie the triangle down on the line so that one side is extended by it. The stud ...
... An informal proof that is often used is the process of having our students create a triangle on a piece of paper, naming the three angles A, B, and C. Cut out the triangle and then draw a line on a piece of paper and then lie the triangle down on the line so that one side is extended by it. The stud ...
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.