Introduction to Logic and Euclidean Geometry

Introduction

This unit bundles student expectations that address distances in one-dimensional systems, constructions of congruent line segments and congruent angles, and the structure of a mathematical system, including undefined terms, definitions, postulates and conjectures. The unit also incorporates deductive reasoning to analyze conditional and related statements and to verify conjectures. 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 lay the foundation for geometry by developing an understanding of the structure of a geometric system through examination of the relationship between undefined terms (point, line, and plane), definitions, conjectures, and postulates. Students examine one-dimensional distance relationships in line segments, including fractional distances and midpoints, and make connections to the number line and segment addition. They also examine relationships in rays and angles making connections to the angle measure and angle addition. Constructions are used to explore and make conjectures about congruent geometric relationships in line segments and angles. They connect their understanding of definitions and postulates of lines, angles, and other geometric vocabulary to the context of the real world. Students also investigate logic statements and the conditions that make them true or false. Students explore conditional statements and their related statements (converse, inverse, and contrapositive) in both a real world and mathematical setting to develop an understanding of logic and the role it plays in geometry and the real world. Students are expected to recognize the connection between a biconditional statement and a true conditional statement with a true converse. Deductive reasoning and inductive reasoning are introduced and applied to make conjectures. Students verify that a conjecture is false using counterexamples.