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Geometry Triangle Questions and Proofs, Triangle Congruency Notes

Learn about triangle properties, angles, sides, and congruency. Review SSS, SAS, ASA, AAS, HL theorems. Practice problems and examples provided.

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Geometry Triangle Questions and Proofs, Triangle Congruency Notes

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  1. In triangle ABC, answer the following questions: • What side is opposite angle A? • What angle is opposite side AB? • What angle is included between sides AC and BC? • What side is included between angles A and C? • What is another way to write angle C? Warmup B A C

  2. How can we use AAS and HL to prove triangles congruent? Agenda: Review SSS, SAS, ASA AAS and HL notes/practice Quiz Tomorrow

  3. Practice (from yesterday) • Textbook p. 245 #9 – 26 • Textbook p. 254 #10 – 14, 16, 17, 19, 21

  4. Determine what is missing in order to use the indicated reason

  5. AAS Theorem If two angles and one of the non-included sides in one triangle are congruent to two angles and one of the non-included sides in another triangle, then the triangles are congruent.

  6. AAS Looks Like… A G F A: ÐK @ÐM A: ÐKJL @ÐMJL S: JL @ JL DJKL @DJML J B C D A: ÐA @ÐD A: ÐB @ÐG S: AC @ DF ACB  DFG M K L

  7. AAS vs. ASA AAS ASA

  8. Parts of a Right Triangle hypotenuse legs

  9. HL TheoremRIGHT TRIANGLES ONLY! If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

  10. W HL Looks Like… M N T X V Right Ð: ÐTVW & ÐXVW H: TW @ XW L: WV @ WV Right Ð: ÐM & ÐQ H: PN @ RS L: MP @ QS P R NMP  RQS WTV  WXV Q S

  11. There’s no such thing as AAA AAA Congruence: These two equiangular triangles have all the same angles… but they are not the same size!

  12. Recap: There are 5 ways to prove that triangles are congruent: SSS SAS ASA AAS HL

  13. Examples M D N L A: ÐL @ÐJ A: ÐM @ÐH S: LN @ JK H A C B B is the midpoint of AC J S: AB @ BC A: ÐABD @ÐCBD S: DB @ DB AAS K SAS DMLN @ DHJK DABD @ DCBD

  14. Examples B C A C B E D D A DB ^ AC AD @ CD HL A: ÐA @ÐC S: AE @ CE A: ÐBEA @ÐDEC DABD @ DCBD Right Angles: ÐABD & ÐCBD H: AD @ CD L: BD @ BD ASA DBEA @ DDEC

  15. Examples W Z B A C X V D A: ÐWXV @ÐYXZ S: WV @ YZ Y B is the midpoint of AC SSS DDAB @ DDCB Not Enough! We cannot conclude whether the triangle are congruent. S: AB @ CB S: BD @ BD S: AD @ CD

  16. Practice • Textbook p. 254 #15, 18, 25 • Textbook p. 260 # 1-12, 15-23

  17. State if the two triangles are congruent and state the reason (SSS, SAS, ASA, AAS, HL) 2. 1. 4. 3.

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