Parallel and Perpendicular Lines
... 16. MP 2, 3 The lines a, b, c, and p are coplanar. a is perpendicular to p, b is perpendicular to p, and c intersects a. Do lines b and c intersect? Make a sketch and explain your answer. 17. MP 2, 4 5th and 10th Avenues are parallel; K Street runs parallel to J Street. Lincoln Way is perpendicular ...
... 16. MP 2, 3 The lines a, b, c, and p are coplanar. a is perpendicular to p, b is perpendicular to p, and c intersects a. Do lines b and c intersect? Make a sketch and explain your answer. 17. MP 2, 4 5th and 10th Avenues are parallel; K Street runs parallel to J Street. Lincoln Way is perpendicular ...
Parallel and Perpendicular Lines
... Lines must be marked parallel with the arrows in order to say they are parallel. Just because two lines LOOK parallel, does not mean that they are. Recall the definition of perpendicular from Chapter 1. Two lines are perpendicular when they intersect to form a 90◦ angle. Below l ⊥ AB. ...
... Lines must be marked parallel with the arrows in order to say they are parallel. Just because two lines LOOK parallel, does not mean that they are. Recall the definition of perpendicular from Chapter 1. Two lines are perpendicular when they intersect to form a 90◦ angle. Below l ⊥ AB. ...
Congruent Triangles - TEACHER
... Any line with a single tick mark, is congruent to all other lines with a single tick mark. Double or triple tickets marks work in the same way, but in no means tells you which line is bigger. Since we notice pair of sides (on the vertical lines) ___S___ And we notice the next angle (both rights) ___ ...
... Any line with a single tick mark, is congruent to all other lines with a single tick mark. Double or triple tickets marks work in the same way, but in no means tells you which line is bigger. Since we notice pair of sides (on the vertical lines) ___S___ And we notice the next angle (both rights) ___ ...
Conjectures for Geometry for Math 70 By I. L. Tse Chapter 2
... 1. Triangle Sum Conjecture – the sum of the measures of angles in every triangle is 180°. 2. Isosceles Triangle Conjecture: If a triangle is isosceles, then its base angles are congruent. 3. Converse of the Isosceles Triangle Conjecture: If a triangle has two congruent angles, then the triangle is ...
... 1. Triangle Sum Conjecture – the sum of the measures of angles in every triangle is 180°. 2. Isosceles Triangle Conjecture: If a triangle is isosceles, then its base angles are congruent. 3. Converse of the Isosceles Triangle Conjecture: If a triangle has two congruent angles, then the triangle is ...
Task - Illustrative Mathematics
... For quadrilaterals, on the other hand, these nice tests seem to be lacking. This task addresses this issue for a specific class of quadrilaterals, namely parallelograms. This task is ideal for hands-on work or work with a computer to help visualize the possibilities. It turns out that knowing all fo ...
... For quadrilaterals, on the other hand, these nice tests seem to be lacking. This task addresses this issue for a specific class of quadrilaterals, namely parallelograms. This task is ideal for hands-on work or work with a computer to help visualize the possibilities. It turns out that knowing all fo ...
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.