7.1 Introduction

Description

Quick Overview

This section introduces the concept of triangles, their properties, and lays the foundation for the study of congruence in triangles.

Standard

In this section, students are reminded about the basic properties of triangles, such as their definition and essential components, including sides, angles, and vertices. The section sets the stage for an in-depth exploration of triangle congruence, including various properties and inequalities related to triangles.

Detailed

Introduction to Triangles

This section introduces triangles as a fundamental geometric shape formed by three intersecting lines, defined by three sides, three angles, and three vertices. For instance, a triangle labeled as

delta ABC, where AB, BC, and CA are the sides and angles are denoted as ∠A, ∠B, ∠C. The relationships between the sides and angles are pivotal as they contribute to properties explored in this chapter, specifically focusing on the congruence of triangles. The significance and applications of congruence are highlighted through everyday examples—such as identical photographs and congruent shapes in objects we use daily. Using these examples, students are encouraged to consider additional instances of congruent figures, preparing them for deeper investigations into congruence rules and triangle properties.

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Key Concepts

  • Triangles: Defined as a figure with three sides, three angles, and three vertices.

  • Congruence: The property that two figures are identical in shape and size.

Memory Aids

🎵 Rhymes Time

  • Triangles have three sides, it's plain to see, with angles and vertices, just like A, B, C.

📖 Fascinating Stories

  • Imagine a little triangle named Trixie, who loved to play with her friends Circle and Square, always joining together to create beautiful shapes.

🧠 Other Memory Gems

  • Remember 'Tri' for triangle, because 'Tri' means three!

🎯 Super Acronyms

TAV - Triangle, Angles, Vertices

Glossary of Terms

  • Term: Triangle

    Definition:

    A closed figure formed by three intersecting lines.

  • Term: Congruent Figures

    Definition:

    Figures that are equal in shape and size.

  • Term: Vertices

    Definition:

    The points where the sides of a triangle intersect.

  • Term: Angles

    Definition:

    The measure of the turn between two lines extending from a common point.