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Sections 4.3 - 4.5

Sections 4.3 - 4.5. Triangle Congruence. Example 1:. Assume that G is the midpoint of . Explain whether or not ∆FGJ and ∆HGJ are congruent. ∆FGJ  ∆HGJ by SSS. On Your Own 1:. Decide whether or not the congruent statement is true. Explain your reasoning. a. b.  by SSS.

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Sections 4.3 - 4.5

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  1. Sections 4.3 - 4.5 Triangle Congruence

  2. Example 1: Assume that G is the midpoint of . Explain whether or not ∆FGJ and ∆HGJ are congruent. ∆FGJ  ∆HGJ by SSS

  3. On Your Own 1: Decide whether or not the congruent statement is true. Explain your reasoning. a. b.  by SSS Not  by SSS

  4. Example 2: Use the diagram to name the included angle between the given pair of sides. a. b. c. HGI HIG H

  5. On Your Own 2: Use the diagram to name the included angle between the given pair of sides. a. b. c. J HGI GIJ

  6. congruent • Leg: • Hypotenuse: 2 shorter sides of a right triangle Longest side of a right triangle and opposite the right angle

  7. Example 3a Decide whether enough information is given to prove that the triangles are congruent by using SAS.

  8. Example 3b Decide whether enough information is given to prove that the triangles are congruent by using SAS. Not enough info

  9. Example 4: Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem. B)B and  D are both right angles. C is the midpoint of . A)

  10. On Your Own 4: Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem. c. d.

  11. Example 5: Identify congruent triangles Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. a. b. c. Yes AAS NO AAA Yes ASA

  12. On Your Own 5: Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. c. TSW  WVT? d. Yes ASA NO

  13. Combining All the Congruence Theorem Postulates Are the 2 triangles congruent?

  14. Nope, AAA does notinsure that triangles congruent AAS congruence theorem

  15. ASA congruence theorem Reflexive Property HL congruence theorem

  16. AAS congruence theorem e) AAScongruence theorem f) D F B E C A

  17. No theorem to prove the 2 triangles congruent g) SSS congruence theorem h) Reflexive Property

  18. SAS congruence theorem i) Reflexive Property

  19. Decide whether enough information is given to prove that the triangles are congruent(STATE THE CONGRUENCE THEOREM!) j. k. SSS SAS

  20. Decide whether enough information is given to prove that the triangles are congruent(STATE THE CONGRUENCE THEOREM!) l. m. NO NO

  21. EXTRA PRACTICE Explain how you can prove that the indicated triangles are congruent using the given postulate or theorem. a. b. c.

  22. Practice problems State the third congruence that is needed to prove that ∆ DEF ∆ ABC, using the given postulate or theorem. 1. 2. 3.  E   B

  23. Tell whether you can use the given information to show that ∆ JKL  ∆ RST. 4. 5. 6. 7. NO Yes AAS Yes ASA NO

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