Pythagorean Theorem and Converse – 2025/2026 Exam Questions with Verified Answers | Right Triangles, Hypotenuse, and Triangle Classification

This document features a comprehensive collection of graded and verified exam questions and answers on the Pythagorean Theorem and its Converse, specifically tailored for the 2025/2026 academic year. It provides clear, accurate explanations of triangle side relationships, square roots, and the application of the theorem in problem-solving. Included in this resource: Calculation of the hypotenuse using the Pythagorean Theorem (e.g., given legs a = 3, b = 4) Converse checks to determine if given side lengths form a right triangle (e.g., 8, 15, 17 = Yes; 24, 25, 17 = No) Concept definitions, such as right angle, legs, hypotenuse, square, and perfect square Mathematical operations and vocabulary, including inverse operations Historical reference to Pythagoras and the theorem's earlier uses in Babylonian and Indian mathematics Multiple practice problems with numeric solutions that reinforce understanding of geometric relationships This document is ideal for: Middle school and high school math students (Grades 8–11) Students preparing for standardized tests such as PSAT, SAT, ACT, or state math exams Geometry, Algebra I, or Integrated Math courses Tutors and teachers looking for ready-made practice or assessment material on right triangles Whether you're reviewing for an exam or practicing problem-solving techniques, this study guide delivers concise and correct applications of one of geometry’s most foundational theorems. Keywords: Pythagorean Theorem, hypotenuse calculation, triangle classification, right triangle, legs of a triangle, perfect squares, triangle side lengths, converse of Pythagorean Theorem, geometry exam questions, triangle formulas, math test review, right angle, square root, Pythagoras history