1 / 12

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

jeff
Télécharger la présentation

Proving Triangles Congruent

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related