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Proving Triangles Congruent

Proving Triangles Congruent. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. How much do you need to know. . . . . . about two triangles to prove that they are congruent?.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent

  2. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape.

  3. How much do you need to know. . . . . . about two triangles to prove that they are congruent?

  4. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D 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 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 If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent

  7. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included side 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. Included Angle The angle between two sides H G I

  9. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y

  10. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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

  12. E Y S Included Side Name the included angle: Y and E E and S S and Y YE ES SY

  13. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side If 2 angles and a non-included side of 1 triangle are congruent to 2 angles and the corresponding non-included side of another triangle, then the 2 triangles are congruent

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

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

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

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

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

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

  20. HW: Name That Postulate (when possible)

  21. HW: Name That Postulate (when possible)

  22. Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:

  23. Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

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