Non-Euclidean Geometry Unit
... through the point that is in the same plane as the given line and never intersects it. In spherical geometry there are no such lines. In hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given lin ...
... through the point that is in the same plane as the given line and never intersects it. In spherical geometry there are no such lines. In hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given lin ...
Transformation geometry
... figures as well as recognise given transformations. Initially, some learners might need to make copies of the figures and to physically manipulate these, but visualisation of the movements should be encouraged. Computer software packages such as Sketchpad can be used to study transformations. Some r ...
... figures as well as recognise given transformations. Initially, some learners might need to make copies of the figures and to physically manipulate these, but visualisation of the movements should be encouraged. Computer software packages such as Sketchpad can be used to study transformations. Some r ...
2014-2015 READING Instructional Curriculum Plan Grade: 9
... MACC.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e ...
... MACC.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e ...
2014-2015 MATH Instructional Curriculum Plan Grade: 9
... MACC.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e ...
... MACC.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e ...
Verifying Triangle Congruence Resource
... Name: Period: Date: Verifying Triangles are Congruent Definition of Congruent Triangles - Triangles are congruent if and only if their corresponding sides have equal lengths and their corresponding angles have equal measures. Directions: 1. Create a transformation using the triangle with vertices A( ...
... Name: Period: Date: Verifying Triangles are Congruent Definition of Congruent Triangles - Triangles are congruent if and only if their corresponding sides have equal lengths and their corresponding angles have equal measures. Directions: 1. Create a transformation using the triangle with vertices A( ...
The SMSG Axioms for Euclidean Geometry
... Then 3 angles and 3 sides. But we all know the Euclidean shortcut: SAS. Would it surprise you to know that the shortcut does NOT always work in TCG? Let’s look at two situations: one where it does work and one where it doesn’t and see if we can figure out a way to predict when it’s safe to use the s ...
... Then 3 angles and 3 sides. But we all know the Euclidean shortcut: SAS. Would it surprise you to know that the shortcut does NOT always work in TCG? Let’s look at two situations: one where it does work and one where it doesn’t and see if we can figure out a way to predict when it’s safe to use the s ...
High School Geometry
... Specify a sequence of transformations that will carry a given figure onto another. (MA10‐GR.HS‐S.4‐GLE.1‐EO.a.viii) (CCSS: G‐CO.5) PARCC Calculator neutral o e.g., graph paper, tracing paper, or geometry software. Prove theorems about lines, angles, triangles, and parallelograms. (MA10‐GR.HS‐S.4 ...
... Specify a sequence of transformations that will carry a given figure onto another. (MA10‐GR.HS‐S.4‐GLE.1‐EO.a.viii) (CCSS: G‐CO.5) PARCC Calculator neutral o e.g., graph paper, tracing paper, or geometry software. Prove theorems about lines, angles, triangles, and parallelograms. (MA10‐GR.HS‐S.4 ...
Spherical Geometry Activities - Notes
... Draw two different points on the sphere and label them A and B. Use your spherical ruler to connect the points with the shortest possible path. Finally, continue drawing the path along the spherical ruler and extend it as far as possible in both directions. 8) In the last part of your construction, ...
... Draw two different points on the sphere and label them A and B. Use your spherical ruler to connect the points with the shortest possible path. Finally, continue drawing the path along the spherical ruler and extend it as far as possible in both directions. 8) In the last part of your construction, ...
Solutions 13-14 - Durham University
... 14.10 (*) We have proved that an isometry fixing 3 points of the absolute is identity map. How many isometries fix two points of the absolute? Solution: We will work in the upper half-plane model. Let f be an isometry fixing two points of the absolute. First, we can conjugate f by an isometry h whic ...
... 14.10 (*) We have proved that an isometry fixing 3 points of the absolute is identity map. How many isometries fix two points of the absolute? Solution: We will work in the upper half-plane model. Let f be an isometry fixing two points of the absolute. First, we can conjugate f by an isometry h whic ...
Honors Geometry Yearlong Curriculum Map
... transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Experiment with G-CO.2 Represent transformations in the plane using, tra ...
... transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Experiment with G-CO.2 Represent transformations in the plane using, tra ...
A Formula for the Intersection Angle of Backbone Arcs with the
... line is the set of points satisfying xℓx + yℓy − zℓz = 0. ...
... line is the set of points satisfying xℓx + yℓy − zℓz = 0. ...
