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Proving Triangles Congruent Free powerpoints at  http://www.worldofteaching.com
Two geometric figures with exactly the  same size and shape. The Idea of a Congruence A C B D E F
How much do you  need to know. . . . . . about two triangles  to prove that they  are congruent?
In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Corresponding Parts  ABC        DEF B A C E D F ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Do you need  all six ? NO !
Side-Side-Side (SSS) ,[object Object],[object Object],[object Object], ABC        DEF B A C E D F
Side-Angle-Side (SAS) ,[object Object],[object Object],[object Object], ABC        DEF B A C E D F included  angle
The angle  between  two sides Included Angle    G    I    H
Name the  included  angle: Y E  and  E S E S  and Y S Y S and  Y E Included Angle    E    S    Y S Y E
Angle-Side- Angle  (ASA) ,[object Object],[object Object],[object Object], ABC        DEF B A C E D F included  side
The side  between  two angles Included Side GI HI GH
Name the  included  side:  Y and   E  E and   S  S and   Y Included Side YE ES SY S Y E
Angle-Angle-Side (AAS) ,[object Object],[object Object],[object Object], ABC        DEF B A C E D F Non-included  side
Warning:  No SSA Postulate A C B D E F NOT CONGRUENT There is no such thing as an SSA postulate!
Warning:  No AAA Postulate A C B D E F There is no such thing as an AAA postulate!  NOT CONGRUENT
The Congruence Postulates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Name That Postulate SAS ASA SSS SSA (when possible)
Name That Postulate (when possible) ASA SAS AAA SSA
Name That Postulate (when possible) SAS SAS SAS Reflexive Property Vertical Angles Vertical Angles Reflexive Property SSA
Name That Postulate (when possible)
(when possible) Name That Postulate
Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA:  For SAS:  B      D For AAS:  A      F AC     FE
Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA:  For SAS: For AAS:
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS.  If it is not possible to prove that they are congruent, write  not possible . Δ GIH     Δ JIK by AAS Ex 4 G I H J K
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS.  If it is not possible to prove that they are congruent, write  not possible . Δ ABC     Δ EDC by ASA Ex 5 B A C E D
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS.  If it is not possible to prove that they are congruent, write  not possible . Δ ACB     Δ ECD by SAS B A C E D Ex 6
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS.  If it is not possible to prove that they are congruent, write  not possible . Δ JMK     Δ LKM by SAS or ASA J K L M Ex 7
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS.  If it is not possible to prove that they are congruent, write  not possible . Not possible K J L T U Ex 8 V
WORK

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Proving Triangles Congruent Sss, Sas Asa

  • 1. Proving Triangles Congruent Free powerpoints at http://www.worldofteaching.com
  • 2. Two geometric figures with exactly the same size and shape. The Idea of a Congruence A C B D E F
  • 3. How much do you need to know. . . . . . about two triangles to prove that they are congruent?
  • 4.
  • 5. Do you need all six ? NO !
  • 6.
  • 7.
  • 8. The angle between two sides Included Angle  G  I  H
  • 9. Name the included angle: Y E and E S E S and Y S Y S and Y E Included Angle  E  S  Y S Y E
  • 10.
  • 11. The side between two angles Included Side GI HI GH
  • 12. Name the included side:  Y and  E  E and  S  S and  Y Included Side YE ES SY S Y E
  • 13.
  • 14. Warning: No SSA Postulate A C B D E F NOT CONGRUENT There is no such thing as an SSA postulate!
  • 15. Warning: No AAA Postulate A C B D E F There is no such thing as an AAA postulate! NOT CONGRUENT
  • 16.
  • 17. Name That Postulate SAS ASA SSS SSA (when possible)
  • 18. Name That Postulate (when possible) ASA SAS AAA SSA
  • 19. Name That Postulate (when possible) SAS SAS SAS Reflexive Property Vertical Angles Vertical Angles Reflexive Property SSA
  • 20. Name That Postulate (when possible)
  • 21. (when possible) Name That Postulate
  • 22. Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS:  B   D For AAS:  A   F AC  FE
  • 23. Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
  • 24. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible . Δ GIH  Δ JIK by AAS Ex 4 G I H J K
  • 25. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible . Δ ABC  Δ EDC by ASA Ex 5 B A C E D
  • 26. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible . Δ ACB  Δ ECD by SAS B A C E D Ex 6
  • 27. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible . Δ JMK  Δ LKM by SAS or ASA J K L M Ex 7
  • 28. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible . Not possible K J L T U Ex 8 V
  • 29. WORK