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…

B C D

FGA

ACB DFG

A: A DA: B GS: AC DF

J

K LM

A: K MA: KJL MJLS: JL JLJKL JML

AAS vs. ASA

ASAAAS

Parts of a Right Triangle

legs

hypotenuse

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.

HL Looks Like…

XTV

W

WTV WXV

NMP RQS

NM

P

SQ

R

Right : M & QH: PN RSL: MP QS

Right : TVW &

XVW

H: TW XW

L: WV WV

There’s no such thing as AAAAAA Congruence:

These two equiangular triangles have all the same angles… but they are not the same size!

Recap:

There are 5 ways to prove that triangles are congruent:

SSS

SAS

ASA

AAS

HL

Examples

A B C

D

B is the midpoint of AC

SAS ABD CBDK

J

LN

M

H

AAS

MLN HJK

S: AB BCA: ABD CBDS: DB DB

A:L JA: M HS: LN JK

Right Angles: ABD & CBDH: AD CDL: BD BD

Examples C

DA

B

E

B C

D

A

DB AC AD CD

HL

ABD CBDA: A CS: AE CEA: BEA DEC

ASA

BEA DEC

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 CBS: BD BDS: AD CD

A: WXV YXZS: WV YZ