HSMTH 30 HSMTH 30 - MiraCosta College
... 2). Identify location, length, and midpoint of segments 3). Apply congruence and addition properties of segments and angles 4). Calculate angle measurement using properties of special angles (i.e., vertical, complementary, and supplementary) 5). Classify triangles by sides and/or angles 6). Calculat ...
... 2). Identify location, length, and midpoint of segments 3). Apply congruence and addition properties of segments and angles 4). Calculate angle measurement using properties of special angles (i.e., vertical, complementary, and supplementary) 5). Classify triangles by sides and/or angles 6). Calculat ...
Lesson 4.1 File
... bridges to high-rise buildings. One such property of triangles is their rigidity. Another application of triangles is a procedure used in surveying called triangulation. This procedure allows surveyors to ___________ points or positions on a map by measuring angles and distances and creating a netwo ...
... bridges to high-rise buildings. One such property of triangles is their rigidity. Another application of triangles is a procedure used in surveying called triangulation. This procedure allows surveyors to ___________ points or positions on a map by measuring angles and distances and creating a netwo ...
Polygons 7.1 Triangle Application Theorems
... two triangles such that two ______and a ___________side of one are congruent to the corresponding parts of the other, then the triangles are congruent. ( AAS) Given: ∠ G ≅ ∠ K ∠ H ≅ ∠ M Prove: Δ GHJ ≅ Δ KMO ...
... two triangles such that two ______and a ___________side of one are congruent to the corresponding parts of the other, then the triangles are congruent. ( AAS) Given: ∠ G ≅ ∠ K ∠ H ≅ ∠ M Prove: Δ GHJ ≅ Δ KMO ...
3 Similarity theorems
... The middle triangle has all its lengths half as big as those of 4ABC. So applying SSS (with k = 12 ) we deduce that 4LM N ∼ 4ABC. The vertices are listed in the correct order, so it is ∠LN M that corresponds to ∠C. We know (by B3) that the straight angle ∠AN B is the sum α+β +γ of the three angles ...
... The middle triangle has all its lengths half as big as those of 4ABC. So applying SSS (with k = 12 ) we deduce that 4LM N ∼ 4ABC. The vertices are listed in the correct order, so it is ∠LN M that corresponds to ∠C. We know (by B3) that the straight angle ∠AN B is the sum α+β +γ of the three angles ...
2 and 3 Dimensional Figures
... Two-dimensional figures have only two dimensions: height and width. A polygon is a two-dimensional figure that has straight sides and is closed. Polygon is a word that comes from the Greek language and means “many” for “poly” and “angles” for “gon.” All of the plane figures, which will be described ...
... Two-dimensional figures have only two dimensions: height and width. A polygon is a two-dimensional figure that has straight sides and is closed. Polygon is a word that comes from the Greek language and means “many” for “poly” and “angles” for “gon.” All of the plane figures, which will be described ...
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.