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Focus : How can we prove triangles congruent?

Focus : How can we prove triangles congruent?. Do Now: From what you remember, list some methods of proving triangles congruent. HW: Workbook pg 67 # 2, 8. SSS. All three corresponding sides are congruent. A. B. D. C. SSS – Practice Try solving using the Side-Side-Side method.

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Focus : How can we prove triangles congruent?

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  1. Focus: How can we prove triangles congruent? Do Now: From what you remember, list some methods of proving triangles congruent. HW: Workbook pg 67 # 2, 8

  2. SSS • All three corresponding sides are congruent

  3. A B D C SSS – PracticeTry solving using the Side-Side-Side method Given : Rectangle ABCD Prove : ▲ABC ▲ACD

  4. ASA • Two angles and an included side are congruent.

  5. ASA – PracticeTry solving using the Angle-Side-Angle method Given : BC bisects Angles ABC and ADC Prove : ▲ABD▲BCD A B D C

  6. SAS • Two sides and an included angle are congruent

  7. SAS- PracticeTry solving using the Side-Angle-Side method Given : - Angles ADB and CDB are right angles -ADDC Prove: Triangles ABD and BCD are congruent. B A C D

  8. AAS • Two sides and a non-included angle are congruent *Note: I made a mistake on the worksheet – the diagram for AAS is actually supposed to look like this:

  9. E D C B A F AAS- PracticeTry solving using the Angle-Angle-Side method Given- AC  BD - ED ║ AF - Angle AFB  Angle CED

  10. Hy-Leg  Hy-Leg • Two right triangles are congruent if their hypotenuse and one leg are congruent.

  11. Hy-Leg - PracticeTry solving using the Hy-Leg  Hy-Leg method Given: - Right triangles ABD and CDB -Angle BAD  Angle BCD Prove: Triangle ABD  Triangle BCD B C A D

  12. Worksheet • Complete the worksheet in groups.

  13. 1. GIVEN: Worksheet Which method can NOT be used to prove ? a-SSS b-SAS c-AAS d-HL e-ASA

  14. Worksheet (cont.)

  15. 2.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.  3.   Is ABC DBC? If so, name the postulate or theorem used.  1.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.  4.  List the methods of proving triangles congruent.   5.  Does HL imply that SSA can be used to prove triangle congruent? Explain your answer.   6. Which of the following is NOT a valid test for congruent triangles?  SSA,  ASA , AAS , or SAS 

  16. 7.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.  8.  State whether or not each of the following triangle pairs is congruent. If so, state a reason.  9. Given: B is the midpoint of FC. AB and FD bisect each other. AD  BC  Prove: angle ADF  angle F  10. Is ABC DEC? If so, name the postulate or theorem used.  11.   Given: BD is the median of AC. BA  BCProve: ABD CBD  12. Given: ABBE, EFBE, BC DE, AD CFProve: Angle A  Angle F 

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