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Geometry 5-6 ASA and AAS

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This document discusses two postulates for proving triangles congruent: 1. Angle-Side-Angle (ASA) postulate - If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. 2. Angle-Angle-Side (AAS) postulate - If two angles and one non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent. The document provides examples of applying these postulates to determine if pairs of triangles are congruent. It also notes there are no AAA or SSA postulates to prove triangles congruent.

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5-6 ASA & AAS
Proving Triangles Congruent jc-schools.net/PPT/geometrycongruence.ppt
Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side
Angle-Side-Angle (ASA) Postulate 8-3: 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.
Angle-Side-Angle (ASA) 1. A   D 2. AB  DE 3.  B   E ABC   DEF included side jc-schools.net/PPT/geometrycongruence.ppt
Before we start…let’s get a few things straight C A B Y X Z INCLUDED SIDE
Included Side The side between two angles GI HI GH
Included Side Name the included side: Y and E E and S S and Y E Y S YE ES SY
Angle-Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included
Angle-Angle-Side (AAS) Theorem 8-1: If two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) 1. A  D 2.  B  E 3. BC  EF ABC   DEF Non-included side jc-schools.net/PPT/geometrycongruence.ppt
Warning: No SSA Postulate B There is no such thing as an SSA postulate! A C E D F NOT CONGRUENT jc-schools.net/PPT/geometrycongruence.ppt
Warning: No AAA Postulate B A C E D F There is no such thing as an AAA postulate! NOT CONGRUENT jc-schools.net/PPT/geometrycongruence.ppt
}Your Only Ways To Prove Triangles Are Congruent
Name That Postulate (when possible) ASA AAA SSA jc-schools.net/PPT/geometrycongruence.ppt
Things you can mark on a triangle when they aren’t marked. Overlapping sides are congruent in each triangle by the REFLEXIVE property Vertical Angles are congruent Alt Int Angles are congruent given parallel lines
Ex 1 ΔDEF ΔLMN D N DE NL In and , , and E L . Write a congruence statement.         D E F   N L M
Ex 2 What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N E N
Ex 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N DL
Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible. ΔGIH  ΔJIK by AAS G I H J K Ex 4
Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible. B A ΔABC  ΔEDC by ASA C D E Ex 5
Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible. J K M L ΔJMK  ΔLKM by SAS or ASA Ex 7
Determine if whether each pair of triangles is congruent by 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

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Geometry 5-6 ASA and AAS

  • 1. 5-6 ASA & AAS
  • 2. Proving Triangles Congruent jc-schools.net/PPT/geometrycongruence.ppt
  • 3. Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side
  • 4. Angle-Side-Angle (ASA) Postulate 8-3: 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.
  • 5. Angle-Side-Angle (ASA) 1. A   D 2. AB  DE 3.  B   E ABC   DEF included side jc-schools.net/PPT/geometrycongruence.ppt
  • 6. Before we start…let’s get a few things straight C A B Y X Z INCLUDED SIDE
  • 7. Included Side The side between two angles GI HI GH
  • 8. Included Side Name the included side: Y and E E and S S and Y E Y S YE ES SY
  • 9. Angle-Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included
  • 10. Angle-Angle-Side (AAS) Theorem 8-1: If two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle, then the two triangles are congruent.
  • 11. Angle-Angle-Side (AAS) 1. A  D 2.  B  E 3. BC  EF ABC   DEF Non-included side jc-schools.net/PPT/geometrycongruence.ppt
  • 12. Warning: No SSA Postulate B There is no such thing as an SSA postulate! A C E D F NOT CONGRUENT jc-schools.net/PPT/geometrycongruence.ppt
  • 13. Warning: No AAA Postulate B A C E D F There is no such thing as an AAA postulate! NOT CONGRUENT jc-schools.net/PPT/geometrycongruence.ppt
  • 14. }Your Only Ways To Prove Triangles Are Congruent
  • 15. Name That Postulate (when possible) ASA AAA SSA jc-schools.net/PPT/geometrycongruence.ppt
  • 16. Things you can mark on a triangle when they aren’t marked. Overlapping sides are congruent in each triangle by the REFLEXIVE property Vertical Angles are congruent Alt Int Angles are congruent given parallel lines
  • 17. Ex 1 ΔDEF ΔLMN D N DE NL In and , , and E L . Write a congruence statement.         D E F   N L M
  • 18. Ex 2 What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N E N
  • 19. Ex 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N DL
  • 20. Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible. ΔGIH  ΔJIK by AAS G I H J K Ex 4
  • 21. Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible. B A ΔABC  ΔEDC by ASA C D E Ex 5
  • 22. Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible. J K M L ΔJMK  ΔLKM by SAS or ASA Ex 7
  • 23. Determine if whether each pair of triangles is congruent by 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