Students perform a hands-on visual proof in Activity 6 where they color, cut, and rearrange the a^2 and b^2 squares to fill the c^2 square, demonstrating that a^2 + b^2 = c^2. Students also use Activity 3 to plug side lengths into a^2 + b^2 = c^2 and decide whether a triangle is right, working through examples (6,8,10 and 7,10,12) that show the test in action. Multiple practice pages ask students to verify triangles and explain answers, giving repeated opportunities to apply the converse idea.

The unit skills list explicitly states that students should "Explain a proof of the Pythagorean Theorem and its converse" and that students should "Understand and apply the Pythagorean Theorem." Multiple student problems require applying the theorem (e.g., finding the hypotenuse given legs 6 and 8, and verifying that triples like 9,12,15 and 10,24,26 form right triangles). The unit review and answer keys include Pythagorean computations and confirmations that certain triples satisfy a^2 + b^2 = c^2.

Activity 4 asks students to write the Pythagorean Theorem, use it to find a hypotenuse (9, 12 → c = 15), determine whether the triangle with sides 8, 15, 17 is a right triangle and "explain how you know," and find the distance between points A(0,0) and B(6,8) showing work with the Pythagorean Theorem. The Parent Plan Skills list explicitly includes "Explain a proof of the Pythagorean Theorem and its converse," indicating the intended learning goal is included in the lesson materials.

Students solve problems that use the Pythagorean relationship: Problem 16 asks students to find the distance between A(0,0) and B(6,8) with answer 10, and Problem 17 asks for the hypotenuse of a right triangle with legs 9 and 12 with answer 15. These items require students to compute lengths using a^2 + b^2 = c^2 and the distance between points on a coordinate plane. Several geometry tasks ask for distances and classifications that rely on the Pythagorean result.