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Understanding Triangle Congruence: Postulates and Properties

This presentation explores the concept of triangle congruence, essential for geometry. It details the conditions necessary to prove triangles are congruent, including the Reflexive Property of Congruence, Side-Side-Side (SSS) Postulate, and Side-Angle-Side (SAS) Postulate. The presentation also covers concepts like included angles and sides and how they relate to triangle congruence. Through definitions and examples, learners will gain insights into how geometric figures can be assessed for similarity in size and shape, which is crucial for various applications in geometry.

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Understanding Triangle Congruence: 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 angle: 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

  14. Homework Work Packet: SSS and SAS

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