Students draw right triangles on coordinate grids between pairs of lattice points, count rise and run, and compute slopes as rise/run. In Activity 2 students set up proportions comparing the rise and run of different right triangles and answer yes/no questions about whether the triangles are similar. The lesson repeatedly has students use triangle side ratios to conclude that triangles with equal rise/run are similar and that points lie on the same straight line.

Students identify and match corresponding angles in Activity 3 (Corresponding Parts) by writing statements like ∠A → ∠R and filling blanks for matching angles. In Activity 4 (Similar Shapes) students are told that similar triangles have equal angles and they use that fact to find a missing angle (e.g., ∠S corresponds to ∠P, so ∠S = 70°). Throughout the lesson students practice writing correspondence statements and using equal-angle relationships to determine similarity and solve for unknown angles.

Students cut out a triangle and line the three corner angles up to form a straight line (Activity 3), providing a hands-on demonstration that the interior angles sum to 180°. Students cut out the two interior angles and place them on the exterior angle to show the exterior angle equals the sum of the two opposite interior angles (Activity 3). Students learn names and properties of angle pairs formed by a transversal (alternate interior/exterior, corresponding, same-side interior, vertical, linear pairs) through notes, diagrams, videos, and practice pages, and they use those relationships to find missing angles in multiple activities. The Angle-Angle (AA) rule is stated and students decide similarity for triangle pairs in practice problems and the quiz (Activity 2 and quiz items).

The Parent Plan skills list explicitly states students should "use informal arguments to establish facts about the angle sum and exterior angle of triangles" and to reason about "angles created when parallel lines are cut by a transversal." Student problems 21–23 ask students to find a missing triangle angle, find an exterior angle, and complete a table of angle measures using rules (VA, S, AI, C, AE). The review problems require students to identify angle relationships (alternate interior, corresponding, vertical, supplementary) and to state the rule used for each angle.

Students are asked to draw two parallel lines with a transversal and to color and identify vertical, alternate interior, alternate exterior, and corresponding angles on the Student Activity page. The project asks students to create and identify two shapes that are similar and to perform a dilation (scale factor 3) on a figure on a coordinate grid, providing practice with similarity and angle-preserving transformations. The Parent Plan explicitly lists the standard wording, including using informal arguments about angle sums, exterior angles, transversal angle relationships, and the angle-angle criterion for similarity.

The Skills section explicitly states: "Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx..." Activity 3 also asks students to find slope from two points and to "Explain how rise over run was used," which requires reasoning about corresponding ratios in triangles.

Activity 3 (Angle Relationships & Triangles) has students compute a missing triangle angle (Problem 3) and solve an exterior-angle problem (Problem 4) with explicit prompt to explain reasoning. The same activity includes several problems (Problems 5–7) where students find corresponding, alternate interior, and supplementary angles when parallel lines are cut by a transversal and are asked to justify their answers. Activity 1 and the Parent Plan include work on similarity and scale factor, so students practice similarity reasoning and computations with similar triangles and dilations.

Students are asked in problem 21 to analyze two lines cut by a transversal: "If one angle measures 65°, find the measures of all related angles," and the answer key identifies vertical, corresponding, alternate interior, and supplementary angles with their measures. Problem 22 asks students to explain how to tell whether two shapes are congruent or similar, and the answer key states that similar shapes have equal corresponding angles and proportional corresponding side lengths.