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Understanding Triangle Congruence: Essential Postulates and Properties

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This presentation explores the concept of triangle congruence in geometry, focusing on essential postulates such as the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. Learn about the reflexive property, which states that a segment or angle is congruent to itself, and how to apply these principles to prove that two triangles are congruent. The material includes clear definitions, diagrams, and examples to illustrate the included angles and sides, providing a comprehensive understanding of triangle congruence fundamentals.

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Understanding Triangle Congruence: Essential Postulates and Properties

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  1. Proving Triangles Congruent jc-schools.net/PPT/geometrycongruence.ppt

  2. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape. jc-schools.net/PPT/geometrycongruence.ppt

  3. How much do you need to know. . . . . . about two triangles to prove that they are congruent? jc-schools.net/PPT/geometrycongruence.ppt

  4. Reflexive Property of Congruence • A segment is congruent to itself. • An angle is congruent to itself.

  5. Side-Side-Side (SSS) Postulate 8-1: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

  6. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF jc-schools.net/PPT/geometrycongruence.ppt

  7. Side-Angle-Side (SAS) Postulate 8-2: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

  8. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle jc-schools.net/PPT/geometrycongruence.ppt

  9. Included Angle The angle between two sides H G I jc-schools.net/PPT/geometrycongruence.ppt

  10. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y jc-schools.net/PPT/geometrycongruence.ppt

  11. Included Side The side between two angles GI GH HI jc-schools.net/PPT/geometrycongruence.ppt

  12. E Y S Included Side Name the included side: Y and E E and S S and Y YE ES SY jc-schools.net/PPT/geometrycongruence.ppt

  13. How are the triangles congruent? Vertical Angles Reflexive Property SAS SAS Vertical Angles SAS jc-schools.net/PPT/geometrycongruence.ppt

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