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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 HL ASA AAS Do you need all six ? NO !

  6. Side-Side-Side (SSS) B E F A C D • 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. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y

  10. Hypotenuse Leg (HL) E A F C B D • AB DE • BE • AC DF ABC DEF right angle

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

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

  13. E Y S Included Side Name the included side: Y and E E and S S and Y YE ES SY

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

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

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

  17. SSS • SAS • HL • ASA • AAS • SSA or ASS • AAA The Congruence Postulates

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

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

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

  21. Name That Postulate (when possible) none Reflexive Property SSS SSA AAA

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

  23. 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:

  24. Try it! MKTU Indicate the additional information needed to enable us to apply the specified congruence postulate. N V For ASA: For SAS: M U For AAS:

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