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# Provingtrianglescongruentssssasasa

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• 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 CongruenceThe Idea of a Congruence A C B DE F
• 3. How much do youHow much do you need to know. . .need to know. . . . . . about two triangles to prove that they are congruent?
• 4. 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 PartsCorresponding Parts ∆ABC ≅ ∆ DEF B A C E D F 1. AB ≅ DE 2. BC ≅ EF 3. AC ≅ DF 4. ∠ A ≅ ∠ D 5. ∠ B ≅ ∠ E 6. ∠ C ≅ ∠ F
• 5. Do you needDo you need all six ?all six ? NO !
• 6. Side-Side-Side (SSS)Side-Side-Side (SSS) 1. AB ≅ DE 2. BC ≅ EF 3. AC ≅ DF ∆ABC ≅ ∆ DEF B A C E D F
• 7. Side-Angle-Side (SAS)Side-Angle-Side (SAS) 1. AB ≅ DE 2. ∠A ≅ ∠ D 3. AC ≅ DF ∆ABC ≅ ∆ DEF B A C E D F included angle
• 8. The angle between two sides Included AngleIncluded Angle ∠ G ∠ I ∠ H
• 9. Name the included angle: YE and ES ES and YS YS and YE Included AngleIncluded Angle SY E ∠ E ∠ S ∠ Y
• 10. Angle-Side-Angle-Side-AngleAngle (ASA)(ASA) 1. ∠A ≅ ∠ D 2. AB ≅ DE 3. ∠ B ≅ ∠ E ∆ABC ≅ ∆ DEF B A C E D F include d side
• 11. The side between two angles Included SideIncluded Side GI HI GH
• 12. Name the included side: ∠Y and ∠E ∠E and ∠S ∠S and ∠Y Included SideIncluded Side SY E YE ES SY
• 13. Angle-Angle-Side (AAS)Angle-Angle-Side (AAS) 1. ∠A ≅ ∠ D 2. ∠ B ≅ ∠ E 3. BC ≅ EF ∆ABC ≅ ∆ DEF B A C E D F Non-included side
• 14. Warning:Warning: No SSA PostulateNo SSA Postulate A C B D E F NOT CONGRUENT There is no such thing as an SSA postulate!
• 15. Warning:Warning: No AAA PostulateNo AAA Postulate A C B D E F There is no such thing as an AAA postulate! NOT CONGRUENT
• 16. The Congruence PostulatesThe Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence
• 17. Name That PostulateName That Postulate SASSAS ASAASA SSSSSSSSASSA (when possible)
• 18. Name That PostulateName That Postulate(when possible) ASAASA SASSAS AAAAAA SSASSA
• 19. Name That PostulateName That Postulate(when possible) SASSAS SASSAS SASSAS Reflexive Property Vertical Angles Vertical Angles Reflexive Property SSASSA
• 20. Name That PostulateName That Postulate(when possible)
• 21. (when possible) Name That PostulateName That Postulate
• 22. Let’s PracticeLet’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. ΔGIH ≅ ΔJIK by AAS G I H J K Ex 4
• 25. ΔABC ≅ ΔEDC by ASA B A C ED Ex 5 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.
• 26. ΔACB ≅ ΔECD 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.
• 27. ΔJMK ≅ ΔLKM by SAS or ASA J K LM 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.
• 28. Not possible K J L T U Ex 8 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. V
• 29. Hypotenuse-Leg Congruence Theorem: HL • Hypotenuse-Leg Congruence Theorem (HL) – If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and the leg of a second right triangle, then the two triangles are congruent. – If ABC and DEF are right triangles, and AC = DF, and BC = EF, then ABC = DEF ~ ~ ~ A B C D E F
• 30. Determine When to Use HL • Is it possible to show that the two triangles are congruent using the HL Congruence Theorem? Explain your reasoning. • The two triangles are right triangles. You know that JH = JH (Hypotenuse). You know that JG = HK (Leg). So, you can use the HL Congruence theorem to prove that JGH = HKJ. G H J K ~ ~ ~
• 31. Triangle Congruence Postulates and Theorems 1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. ASA (Angle-Side-Angle) 4. AAS (Angle-Angle-Side) 5. HL (Hypotenuse-Leg)