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Chapter Outline

In this chapter, you’ll learn how to prove congruence and use congruent figures in real-world situations by understanding and applying geometric principles. Congruence means that two figures have the same size and shape, which can be proven through various transformations such as translations, rotations, and reflections. In real-world situations, proving congruence is essential in fields like architecture, engineering, and design, where ensuring the accuracy and consistency of shapes and structures is crucial. For example, architects use congruent shapes to create symmetrical designs, while engineers rely on congruence to ensure parts fit together perfectly in machinery. By mastering these concepts, you’ll be able to apply congruence to solve practical problems and create precise, reliable designs.

4.1

Congruent Figures

Learning Objectives

By the end of this section, you will be able to:

  • Explore congruent figures

  • Determine if figures are congruent

  • Identify corresponding parts of congruent figures

  • Find unknown measures of congruent figures

4.2

Triangle Congruence - SAS

Learning Objectives

By the end of this section, you will be able to:

  • Examine side-angle-side (SAS) criteria for triangle congruence

  • Prove the SAS congruence theorem

  • Use SAS in triangle proofs

  • Apply SAS to solve problems

4.3

Triangle Congruence - ASA & AAS

Learning Objectives

By the end of this section, you will be able to:

  • Prove ASA and AAS criteria for triangle congruence

  • Use ASA or AAS in triangle proofs

  • Apply ASA or AAS to determine congruence

  • Examine the angle-side-angle (ASA) and angle-angle-side (AAS) criteria for triangle congruence

4.4

Triangle Congruence - SSS & HL

Learning Objectives

By the end of this section, you will be able to:

  • Examine the side-side-side (SSS) and hypotenuse-leg (HL) criteria for triangle congruence

  • Prove SSS and HL for triangle congruence

  • Apply SSS and HL to determine congruence

  • Use SSS and HL in proofs

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