Students practice translating line segments and whole shapes (Problems 3 and 4, Exercises 6–8, Algebraic Translations) by finding new coordinates for endpoints after a given translation rule. The materials state and reinforce that a translation "doesn't change a figure's size or direction," and provide multiple tasks where students apply Ta,b → (x + a, y + b) to lines and rectangles whose sides are parallel. Students compute image coordinates for both endpoints of segments and vertices of polygons, producing original and translated lines and sides on coordinate grids.

Students reflect entire shapes (rectangles, squares, trapezoids, hexagons) and line segments across the x-axis, y-axis, and diagonal lines, plotting original and image vertices and filling tables with before-and-after coordinates (Activities 2, 3, 5, 6). The Parent Plan and several activity answer keys explicitly list that "Lines are taken to lines" and that "Parallel lines are taken to parallel lines," and students use formulas and the perpendicular-distance method to produce corresponding image points.

Students rotate individual line segments (e.g., Line AB, GH, IJ) and plot the images by computing new coordinates and connecting the rotated endpoints. Examples and problems explicitly ask students to find A' and B' for line segments and draw the rotated image, and the lesson repeatedly states that rotations are rigid transformations that preserve lengths and angles. The activities include multiple algebraic rotation problems where students apply coordinate rules to lines and compare original and image coordinates.

The unit skills list explicitly states under transformations: "Parallel lines are taken to parallel lines." The introduction also tells students to "Verify how lines, segments, angles, and parallel lines behave under transformations," and many exercises require students to perform reflections, rotations, translations, and dilations on figures in the coordinate plane. Students work with shapes that have clearly parallel sides (for example, multiple square problems and coordinate-shape transformations), allowing them to observe line behavior after transformations.

The Parent Plan Skills list explicitly names the property "Parallel lines are taken to parallel lines." In Part 2 students draw shapes on a coordinate grid and perform rigid transformations (reflect across an axis, rotate 90° about the origin, and translate using a rule). The Student Activity page directs students to draw "Two parallel lines with a transversal" and to use those for angle-relationship activities.

Students graph pairs of linear equations (for example y = 3x + 1 and y = 3x - 5) and are asked to determine the solution, with answer keys noting these as parallel lines with "no solution." Several problems ask students to compute slopes from two points and identify when two lines have the same slope (e.g., slope = 2) and therefore do not intersect. Images and activity prompts explicitly label pairs of lines as "parallel" and require students to classify systems as one, none, or infinite solutions based on graphing or slope comparison.

The Parent Plan explicitly lists verifying properties of rotations, reflections, and translations and names "Parallel lines are taken to parallel lines." Activity 2 asks students to perform reflections, translations, and rotations on coordinate grids, writing new coordinates and describing how x and y values change. Activity 3 has multiple problems where students identify corresponding and alternate interior angles for parallel lines cut by a transversal, reinforcing understanding of parallelism.

Students perform multiple rigid transformations: they translate a square using T_{1,-3} (problem 11) and translate triangle ABC using T_{-4,2} (problem 14). Students also reflect a point A(5,10) across the y-axis (problem 12) and rotate point B(-3,4) 90° clockwise about the origin (problem 13), giving before-and-after coordinates for transformed figures.