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**Proving Triangles Congruent**

Part 2

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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.

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**AAS Looks Like… A: ÐK @ ÐM A: ÐKJL @ ÐMJL S: JL @ JL DJKL @ DJML**

G F A: ÐM A: ÐMJL S: JL DJML J B C D A: ÐD A: ÐG S: DF ACB DFG M K L

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AAS vs. ASA AAS ASA

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**Parts of a Right Triangle**

hypotenuse legs

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**HL Theorem RIGHT 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.

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**HL Looks Like… Right Ð: ÐTVW & ÐXVW Right Ð: ÐM & ÐQ H: TW @ XW**

N T X V Right Ð: ÐTVW & ÐXVW H: XW L: WV Right Ð: ÐM & ÐQ H: RS L: QS P R NMP RQS WTV WXV Q S

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**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!

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

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**AAS SAS DMLN @ DHJK DABD @ DCBD D A: ÐL @ ÐJ A: ÐM @ ÐH S: LN @ JK A C**

Examples D M N L A: ÐJ A: ÐH S: JK H A C B B is the midpoint of AC J S: BC A: ÐCBD S: DB AAS K SAS DHJK DCBD

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**HL DABD @ DCBD ASA DBEA @ DDEC B A C D A: ÐA @ ÐC S: AE @ CE**

Examples B C A C B E D D A DB ^ AC CD HL A: ÐC S: CE A: ÐDEC DCBD Right Angles: ÐABD & ÐCBD H: CD L: BD ASA DDEC

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**We cannot conclude whether the triangle are congruent.**

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

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Side-side-side (SSS) postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Side-side-side (SSS) postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

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