Understanding Triangles Ms. Gilma Escobar Grade 7
... Note: an angle cannot be obtuse and equilateral at the same time. An equilateral triangle cannot have an obtuse angle because all 3 angles in an equilateral triangle measure 60 degrees. ...
... Note: an angle cannot be obtuse and equilateral at the same time. An equilateral triangle cannot have an obtuse angle because all 3 angles in an equilateral triangle measure 60 degrees. ...
Further Concepts in Geometry
... how large would a 18-inch to 1-foot scale drawing of the Pentagon be? Would such a scale be reasonable? 45. Logical Reasoning Show how you could arrange six toothpicks to form four congruent triangles. Each triangle has one toothpick for each side, and you cannot bend, break, or overlap the toothpic ...
... how large would a 18-inch to 1-foot scale drawing of the Pentagon be? Would such a scale be reasonable? 45. Logical Reasoning Show how you could arrange six toothpicks to form four congruent triangles. Each triangle has one toothpick for each side, and you cannot bend, break, or overlap the toothpic ...
Lesson 14: Congruent Figures
... Learning Target: I can list pairs of corresponding angles and sides on congruent triangles Things that we should know …… The word "congruent" is defined in the dictionary as “identical” in form Congruent figures are the same size and shape. It is possible to turn, flip and/or slide one figure so it ...
... Learning Target: I can list pairs of corresponding angles and sides on congruent triangles Things that we should know …… The word "congruent" is defined in the dictionary as “identical” in form Congruent figures are the same size and shape. It is possible to turn, flip and/or slide one figure so it ...
Handout Page 1 - mvb-math
... 1. Through a point not on a given line, there is exactly one line parallel to the given line. 2. If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 3. If two parallel lines are cut by a transversal, then the alternate interior angles a ...
... 1. Through a point not on a given line, there is exactly one line parallel to the given line. 2. If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. 3. If two parallel lines are cut by a transversal, then the alternate interior angles a ...
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.