PPT-1.6 Rotations and Rotational Symmetry

U se the points G2 4 and H6 6 to answer the following 1 Find the slope of 2 Find the midpoint of 3 Find GH   Warm Up Objectives Identify and draw rotations Identify and describe symmetry in geometric figures. Baldwin armers in ancient cultures as diverse as those of China Greece and Rome shared a common understanding about crop rotations They learned from experience that growing the same crop year after year on the same piece of land resulted in low yiel Suggested reading:. Landau & . Lifshits. , . Quantum Mechanics. , Ch. 12. Tinkham. , . Group Theory and Quantum Mechanics. Dresselhaus. , . Dresselhaus. , . Jorio. , . Group Theory: . Applications to the Physics of Condensed Matter. in . Platonic. . Solids. Polyhedra. A polyhedron is a solid figure bounded by flat faces and straight edges, i.e., by polygons.. Face. . A face of a polyhedron is any of the plane surfaces forming a polyhedron. The faces of a polyhedron are polygons.. Terra Alta/East Preston School. Rotational Symmetry. If, when you rotate a shape, it looks exactly the same as it did in its original position, then we say that the shape has . rotational symmetry. .. Ahhhh. Isn't symmetry wonderful?. Symmetry is all around us. It's in our art, nature and even ourselves. It has been proven that we find things with symmetry more pretty. So in order to have prettier math, we should learn about it, don't you think.. in . Platonic. . Solids. Polyhedra. A polyhedron is a solid figure bounded by flat faces and straight edges, i.e., by polygons.. Face. . A face of a polyhedron is any of the plane surfaces forming a polyhedron. The faces of a polyhedron are polygons.. Euler Theorem + Quaternions . Representing a Point 3D. A three-dimensional point. . A. is a reference coordinate system here. Rotation along the . Z axis. In general:. Using Rotation Matrices. A transformation by which a figure is turned around a fixed point to create an image.. The fixed point that a figure is rotated around.. Lines can be drawn from the . preimage. to the center of rotation and from the center of rotation to the image. . : Hold onto . hw. Using hatch marks create two . pairs figures . that…. . 1. Are congruent. . 2. Are similar . Hatch Marks – notation that shows that the measurements are equal for angles, arcs, line segments, etc. . Topic . 8: Transformational . Geometry. 8-4: Symmetry. Pearson Texas Geometry ©2016 . Holt Geometry Texas ©2007. . TEKS. . Focus:. (3)(D) Identify and distinguish between . reflectional. and rotational symmetry in a plane figure. You drew reflections and rotations of figures. . Identify line and rotational symmetries in two-dimensional figures.. Identify line and rotational symmetries in three-dimensional figures.. Definitions. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. 17.1. 17.2. &. Symmetry. Warm Up. Determine the coordinates of the image of . P. (4, –7) under each transformation. . Identify line and rotational symmetries in two-dimensional figures.. Identify line and rotational symmetries in three-dimensional figures.. Definitions. A figure has . symmetry. is there exists a rigid motion (reflection, translation, rotation, or glide reflection that maps the figures unto itself.. 27-750, Advanced Characterization & Microstructural Analysis. A.D. Rollett, P.N. Kalu. Last revised: 9. th. June, 2009. 2. Objectives. Introduce grain boundaries as a microstructural feature of particular interest..