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Proving Triangles Congruent

Proving Triangles Congruent. Part 2. 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. AAS Looks Like…. A. G. F. A: Ð K @ Ð M

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Proving Triangles Congruent

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  1. Proving Triangles Congruent Part 2

  2. 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.

  3. 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

  4. AAS vs. ASA AAS ASA

  5. Parts of a Right Triangle hypotenuse legs

  6. 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.

  7. 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

  8. 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!

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

  10. 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

  11. 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

  12. 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

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