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4.4 & 4.5 Proving Triangles Congruent

4.4 & 4.5 Proving Triangles Congruent. Interactive notebook Entries. Pg. 17 4-4 & 4-5: Proving Triangles Congruent Pg. 18 Proving Triangles Congruent (Practice). Objectives:. Use the SSS, SAS, ASA, AAS and HL postulates to test for triangle congruence. Corresponding Parts. AB  DE

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4.4 & 4.5 Proving Triangles Congruent

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  1. 4.4 & 4.5 Proving Triangles Congruent

  2. Interactive notebook Entries • Pg. 17 4-4 & 4-5: Proving Triangles Congruent • Pg. 18 Proving Triangles Congruent (Practice)

  3. Objectives: • Use the SSS, SAS, ASA, AAS and HL postulates to test for triangle congruence.

  4. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D In Lesson 4.3, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

  5. SSS SAS ASA AAS HL Do you need all six ? NO !

  6. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF

  7. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle

  8. Included Angle The angle between two sides H G I

  9. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side

  10. Included Side The side between two angles GI GH HI

  11. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side

  12. Hypotenuse-Leg (HL) • ACZX • BC  YX A Z B C X Y ABC ZYX RIGHT TRIANGLES

  13. Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT ALWAYS CONGRUENT

  14. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT ALWAYS CONGRUENT

  15. The Congruence Postulates • SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • HL correspondence • SSA correspondence • AAA correspondence

  16. Name That Postulate (when possible) SAS ASA SSA SSS

  17. Name That Postulate (when possible) AAA ASA SSA SAS

  18. Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS

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