The lesson repeatedly states that congruent shapes match exactly and that corresponding parts remain in the same relative position even if a shape is flipped or rotated (e.g., "even if one shape is flipped, rotated, or resized"). Students practice identifying congruent pairs that are rotated or flipped and use hash marks and angle arcs to match corresponding sides and angles in activities. The text also introduces the idea of rigid transformations by name ("flips, turns, and slides") and notes these moves do not change shape or size.

Students practice sliding points, line segments, and triangles on coordinate grids and labeling images (A → A') using translation notation T_{a,b}. They apply the algebraic rule (x, y) → (x + a, y + b) in worked examples and exercises and compute new coordinates for many given translation rules. Students also analyze given original-and-image pairs and write the translation that maps one to the other (Part 3: "What Was the Move?" and Algebraic Translations problems asking for the rule).

Students practice reflecting points, line segments, and whole shapes across the x-axis, y-axis, y = x, and y = -x using graphing, the Perpendicular Distance Method, and coordinate formulas. Students plot original vertices, apply coordinate rules or measure perpendicular distances, connect reflected vertices, label image points with primes, and check that reflected images are congruent to the originals. The Parent Plan and introductions also direct students to explore rigid transformations generally (reflections, translations, rotations) and to verify properties like preserving lengths and angles.

Students repeatedly apply and identify 90°, 180°, and 270° rotations about the origin using coordinate rules ((x,y)→(−y,x), (y,−x), (−x,−y)) in multiple activity pages and examples. Several problems require students to name the direction and degree of rotation and to compute and plot image coordinates (e.g., rotating points, line segments, and triangles). The text explicitly states that rotations are rigid transformations that keep lengths and angles the same and refers to congruence in the context of rotations.

Students perform given sequences of translations, reflections, and rotations on coordinate grids (e.g., the "Simple Rigid Transformation Sequences" page with explicit moves and vertices) and label resulting images. Activity 2 asks students to be shown pairs of congruent figures and fill in "Move 1," "Move 2," etc., to describe a sequence that maps one figure to the other, with an answer key showing valid sequences. The text and parent notes instruct students to check that side lengths and angles remain the same after each rigid transformation and emphasize that order of moves matters.

Students perform and describe sequences that include rotations, reflections, and translations (for example: rotate a triangle 90° about the origin then translate 2 right and 3 up; rotate 270°; rotate 90° then reflect across the y-axis). The "What Happened?" activity asks students to examine two shapes and choose or write the sequence of transformations that maps one to the other, and the answer key includes rigid-sequence answers such as "Rotate the triangle 90° counterclockwise about the origin; Translate the result 2 units left and 3 units down." Several student pages require students to graph an original shape and apply a specified rotation/reflection/translation sequence step-by-step.

Students answer quiz questions about congruence and transformations (multiple choice items asking which shapes are congruent and which transformation occurred). Students work on coordinate and graph problems that ask for a sequence of transformations (for example: reflect over the y-axis then translate up 2) and complete items that distinguish rigid transformations from dilations. The lesson answer key explicitly states that a sequence of rigid transformations involves translations, reflections, or rotations.

Students are asked to determine whether pairs of shapes are congruent (e.g., squares and triangles) and to match corresponding sides and angles. Multiple problems require students to perform and record rigid transformations: reflect across y = x and the y-axis, translate using rules like T5,−3, and rotate triangles 90° clockwise or counterclockwise. Several items explicitly ask students to identify the transformation rule that maps one triangle onto another (e.g., "What rotation rule maps triangle ABC onto A'B'C'?"). The unit skills list and parent notes explicitly state that students should recognize congruence via rotations, reflections, and translations and describe the sequence of moves that connects congruent figures.

The Parent Plan Skills list explicitly states that students should "Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them." In Part 2 students draw shapes on a coordinate grid and perform reflections (across an axis), a 90° rotation about the origin, and translations using explicit rules like "move right 4 units and up 2 units." The "Design with Meaning" student page asks students to choose "Two shapes that are congruent and similar," reinforcing identification of congruent figures.

The Parent Plan explicitly lists the target skill using the same language as the standard, stating that a two-dimensional figure is congruent to another if the second can be obtained by rotations, reflections, and translations. In Activity 2 students perform and record rigid transformations: they reflect points and triangles across axes and y=x, translate triangles using a rule, and rotate points and triangles (including applying a 90° counterclockwise rule and a 180° rotation). In Activity 1 students decide whether given rectangles and other shapes are congruent or similar and provide reasoning, and Activity 2 includes problems that ask students to identify the transformation that maps one triangle to another.

Students perform individual rigid motions: they translate a square using T_{1,-3} (problem 11) and translate triangle ABC by T_{-4,2} (problem 14). Students reflect and rotate points: they reflect A(5,10) across the y-axis (problem 12) and rotate B(-3,4) 90° clockwise about the origin (problem 13). Students also are asked to explain how they know whether two shapes are congruent or similar (problem 22) and the answer key gives explicit image mappings (e.g., A→A′ and B→B′).