Students are asked to identify corresponding angles in pairs of shapes that are explicitly described as rotated or flipped (e.g., "Corresponding parts are ALWAYS in the same position … even if one shape is flipped, rotated, or resized"). Activity pages and answer keys require students to write angle-equality statements such as ∠A = ∠D, ∠C = ∠F, and to fill in corresponding-angle pairs on rotated figures. Worked examples and practice problems (Example 1: Congruent Triangles; Similar Shapes problems) have students find missing angles by using the fact that corresponding angles are equal in congruent or similar figures.

Students repeatedly translate points, line segments, and triangles (e.g., triangle X(0,0),Y(2,0),Z(1,2) translated to X',Y',Z') and are told the translated figures are the same size and shape. Activities have students compute new coordinates using Ta,b and compare original and image positions (several problems move whole triangles and line segments). The notes and wrap-up explicitly state that a translation does not change size or orientation and that translated shapes are congruent.

Students are told explicitly that a reflection does not change "angle measures" (Getting Started: "The shape doesn't change size or angle measures"). Students perform many point- and shape-reflection tasks: they plot vertices, reflect each vertex across a line, connect reflected vertices, label primes, and are asked to "check that your reflected shape is congruent to the original." Students also use coordinate rules and digital tools to observe that coordinates change in predictable ways while shapes remain congruent.

Students plot original and rotated points, line segments, and triangles using coordinate rules (e.g., examples and Algebraic Rotations activities that tell students to "Draw and compare the original triangle and its rotated image"). Students are asked to identify the direction and degree of rotations across multiple problems and to use coordinate rules to place rotated images precisely. The materials repeatedly state and prompt students to explain that rotations are rigid transformations that keep lengths and angles the same (e.g., questions asking what stays the same when a figure is rotated and parent notes prompting students to explain why lengths and angles stay the same).

Students perform many rigid transformations (translations, reflections, rotations) on coordinate grids and label corresponding vertices using prime notation. Activity instructions and the parent notes ask students to check that side lengths and angles stay the same after each move. Problem sets require applying sequences of transformations to given figures and producing images (e.g., rotating 90°, reflecting, translating) so students can compare original and image shapes.

Students are repeatedly told that dilations "do not change the angles" and that the image is similar to the original, and they are asked when identifying dilations to check "Are the angles the same?" Students perform dilations on the coordinate plane by multiplying coordinates and plotting A′, B′, C′, which preserves the shape and implicitly preserves angle relationships. Students also compare corresponding side lengths and use proportional reasoning to confirm similarity, reinforcing that angle measures remain unchanged when all coordinates are scaled by the same factor.

Students apply rotations, reflections, and translations in worked examples (e.g., Example 2 shows a 90° clockwise rotation rule and its effect on vertex coordinates). Multiple Student Activity Pages ask students to rotate, reflect, and translate given shapes and to carry out or identify two-step sequences using coordinate rules. Activity 2 asks students to analyze two shapes and determine which transformations (flip, turn, shift) occurred by examining coordinates.

Students answer quiz questions that ask them to identify rigid transformations and determine what stays the same (e.g., Question 4 asks which is not a rigid transformation; Question 5 asks what stays the same after a reflection). Students complete coordinate transformation problems that require performing reflections, translations, and dilations (problems that reflect a point across an axis and translate it, or dilate then reflect a triangle). The quiz answer key explicitly states that reflections are rigid and that "angle measures and side lengths are preserved," linking transformations to preserved angle measure.

The Skills list explicitly states students should "Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure." Multiple student activities require performing transformations (reflect across y = x, reflect across the y-axis, rotate 90° clockwise/counterclockwise, and apply translations such as T5,-3) with coordinate plotting so students produce pre-images and images. Several problems ask students to identify congruent angles and matching angles (e.g., the square congruence task and the triangle congruence/rotation/translation exercises), and the answer keys mark corresponding angles as congruent.

The Skills list explicitly states the property: "Angles are taken to angles of the same measure." In Part 2 (Transformative Art) students draw shapes on a coordinate grid and perform a reflection across an axis, a 90° rotation about the origin, and a translation, giving students opportunities to apply rigid transformations. The Student Activity page also has a Colorful Angle Relationships task where students identify and color pairs of vertical, alternate interior/exterior, and corresponding angles, reinforcing angle concepts.

The Parent Plan Skills explicitly list "Angles are taken to angles of the same measure" as a property to verify. In Activity 2 students perform reflections, rotations, and translations of points and triangles on coordinate grids (e.g., reflect triangle DEF across y = x, rotate triangles 90° and 180°, translate triangle ABC) and are asked to write new coordinates and explain the rules. Directions emphasize that students should focus on how each rigid transformation "moves a figure without changing its size or shape," and one task asks students to identify which transformation is not rigid (dilation).

Students perform coordinate transformations: they translate a square using T_{1,-3}, reflect a point across the y-axis (A(5,10)→A'(−5,10)), rotate a point 90° clockwise about the origin (B(−3,4)→B'(4,3)), and translate triangle ABC (questions 11–14). Students calculate image coordinates for these rotations, reflections, and translations and answer questions about congruence and similarity, with the answer key stating that corresponding angles are equal for congruent and similar shapes. Several diagrams show pre- and post-transformation figures (reflected squares and translated/rotated triangles) for students to work with.