Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.

MAT-10.GM.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and to prove relationships in various geometric figures.

MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.

MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.

MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.

MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative).
Find the values of a, h, and k given the graph of the function.

MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).

MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.

MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.

MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),

reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).

MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.

MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.

MAT-10.GM.15 Use transformations to decide if two given figures are similar. Apply the meaning of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

MAT-10.GM.16 Prove similarity theorems about triangles.

MAT-10.GM.17Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.

MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and
k given the graph of the function. Recognize even and odd functions from their graphs and equations.

MAT-12.NO.18 Multiply a vector by a scalar.

Congruence and Similarity

MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.

MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.

MAT-10.GM.07 Use the definition of congruence, based on rigid motions, to show two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.

MAT-10.GM.08 Prove two triangles are congruent using the congruence theorems.

MAT-10.GM.17Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.