Relationships of Lines & TRAVERSALS

Introduction

This unit bundles student expectations that address special pairs of angles formed when one or more lines are intersected by a transversal. Constructions and manipulatives are used to explore the geometric relationships, and make conjectures by investigating patterns with a focus on parallel lines cut by a transversal and their related angles. Geometric conjectures are tested developing an awareness of the connections between conjectures, postulates, and theorems. 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 explore angle relationships formed by one line and one transversal including vertical angles, linear pairs, and adjacent angles. Students construct congruent angles and a line parallel to a given line through a point not on a line using a compass and a straightedge. Students investigate patterns to make conjectures and define angles formed by parallel lines cut by a transversal. Students explore angle relationships formed by two parallel lines and one or more transversal(s) including corresponding angles, same side interior angles, alternate interior angles, and alternate exterior angles. Students use a variety of tools such as patty paper, folding techniques, etc. to investigate these relationships between angle pairs formed when parallel lines are cut by a transversal(s). Students formulate deductive proofs for conjectures about angles formed by parallel lines and transversals and apply these relationships to solve mathematical and real-world problems. Students explore and apply the converse of theorems and postulates for parallel lines cut by a transversal to solve mathematical and real-world problems.