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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.

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Presentation on theme: "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."— 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… BC D FG A  ACB   DFG A:  A   D A:  B   G S: AC  DF J K L M A:  K   M A:  KJL   MJL S: JL  JL  JKL   JML

4 AAS vs. ASA ASAAAS

5 Parts of a Right Triangle legs hypotenuse

6 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.

7 HL Looks Like… XT V W  WTV   WXV  NMP   RQS N M P SQ R Right  :  M &  Q H: PN  RS L: MP  QS Right  :  TVW &  XVW H: TW  XW L: WV  WV

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 A B C D B is the midpoint of AC SAS  ABD  CBD K J L N M H AAS  MLN  HJK S: AB  BC A:  ABD   CBD S: DB  DB A:  L   J A:  M   H S: LN  JK

11 Right Angles :  ABD &  CBD H: AD  CD L: BD  BD Examples C D A B E B C D A DB  ACAD  CD HL  ABD  CBD A:  A   C S: AE  CE A:  BEA   DEC ASA  BEA  DEC

12 Examples B C D A B is the midpoint of AC SSS  DAB  DCB Z Y X V W Not Enough! We cannot conclude whether the triangle are congruent. S: AB  CB S: BD  BD S: AD  CD A:  WXV   YXZ S: WV  YZ


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