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Proving Triangles Congruent

Proving Triangles Congruent. F. B. A. C. E. D. What does it mean for 2 triangles to be congruent?. Corresponding angles and sides should have the same measure . How much do you need to know. . . . . . about two triangles to prove that they

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Proving Triangles Congruent

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  1. Proving Triangles Congruent

  2. F B A C E D What does it mean for 2 triangles to be congruent? Corresponding angles and sides should have the same measure.

  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 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. But how many do you need? And which ones?

  7. What if we have all three angles? • Use your protractor to draw Triangle ABC., so that: • Angle A measures 70º, • Angle B measures 30º and • Angle C measures 80º. • Now measure the lengths of the sides of your triangle. • Compare your results with your partner. Are your triangles congruent?

  8. Does AAA work? No, the angles will be the same, but the triangles don’t have to be congruent.

  9. Will 3 sides be enough for congruence? • Make a triangle DEF so that: • DE is 5 cm • EF is 8 cm • DF is 12 cm • Now measure the angles. Compare your results with your partner. Are your triangles congruent?

  10. Side-Side-Side (SSS) SSS Congruence Conjecture If the 3 sides of one triangle are congruent to the 3 sides of another triangle then the triangles are congruent.

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

  12. Side-Angle-Side (SAS) SAS Congruence Conjecture If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle then the triangles are congruent.

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

  14. Included Angle The angle between two sides G

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

  16. Included Side The side between two angles GH

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

  18. Angle-Side-Angle (ASA) ASA Congruence Conjecture If 2 angles and the included side of one triangle is congruent to two angles and the included side of another triangle, then the triangles are congruent.

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

  20. Angle-Angle-Side (AAS or SAA) AAS Congruence Conjecture If 2 angles and a non-included side of one triangle is congruent to the corresponding angles and side of another triangle, then the triangles are included

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

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

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

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

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

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

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

  28. HW: Name That Postulate (when possible)

  29. HW: Name That Postulate (when possible)

  30. 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:

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

  32. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

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