Relationships of Right Triangles

Introduction

This unit bundles student expectations that address constructions of right triangles and right triangle relationships including the Pythagorean Theorem, Pythagorean triples, special right triangles, and trigonometric ratios. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

During this Unit

Students concretely explore and prove the Pythagorean Theorem and its converse. Students examine patterns of given Pythagorean triples to discover other Pythagorean triples. Students use constructions of right triangles and their altitudes to investigate and analyze geometric relationships, including geometric mean. Students explore geometric relationships in special right triangles (30°-60°-90° and 45°-45°-90°) and similar triangles. Students develop right triangle trigonometry and trigonometric ratios to determine side lengths and angle measures in right triangles. Students apply all right triangle geometric relationships to solve both mathematical and real-world problem situations.