TRANSFORMATIONAL GEOMETRY



TRANSFORMATIONAL GEOMETRY

Unit Graphic Organizer

What impact does each type of transformation (reflection, rotation, translation, and dilation) have on the location, size, and orientation of geometric objects?

Unit Abstract

The study of transformations in geometry gives students a visual perspective of the outcome of using reflections, rotations, translations, glide reflections, and dilations. Including the task of using coordinates to look for functions rules for each of these transformations helps connect the geometric and algebraic views. When transforming function rules in later algebra courses, the visual perspective and understanding of the effect the transformation has on the coordinates will assist in connecting the geometric and algebraic representations.

The use of a computer software program or graphing calculator with geometric drawing capabilities that allows students to draw and manipulate figures to make conjectures and reach conclusions. In particular, using available software to perform transformations allows students to make conjectures about algebraic or coordinate rules that model transformations.

Students in Geometry Honors will deepen and extend understanding of geometric relationships. Students will use properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge. Algebraic and geometric ideas are tied together. Students will experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Honors students will represent quantities, model, and perform operations using vectors and use matrices to perform operations and solve problems.

Essential Questions:

What are the differences between rigid and non-rigid transformations?

What six properties are preserved (invariant) under a line rotation and translation?

What does one need to know before starting a rotation?

Which transformation is a direct isometry?

What are the similarities and differences between the images and pre-images generated by each of the rigid transformations?

How can transformations be applied to real-world situations?

What is the relationship between the coordinates of the vertices of a figure and the coordinates of the vertices of the figure’s image generated by each of the rigid transformations?

Vocabulary

Image, preimage, rotations, reflections, translations, horizontal stretch, rigid motion, non rigid transformation, isometry, functions, points, planes, distance, angle, inputs, outputs,

direction, line of refection, angle of rotation, translation vector, center of rotation, glide reflections, composition, direct isometry, opposite isometry, inputs, outputs, position vector, vector

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