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Published byAndre Huntsman Modified over 2 years ago

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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… 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

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AAS vs. ASA ASAAAS

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Parts of a Right Triangle legs hypotenuse

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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… 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

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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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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

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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

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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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