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: ÐK @ ÐM A: ÐKJL @ ÐMJL S: JL @ JL DJKL @ DJMLG F
A: ÐM
A: ÐMJL
S: JL
DJML J B C D
A: ÐD
A: ÐG
S: DF
ACB  DFG M K L

4. AAS vs. ASA
AAS
ASA

5. Parts of a Right Triangle
hypotenuse
legs

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… Right Ð: ÐTVW & ÐXVW Right Ð: ÐM & ÐQ H: TW @ XWN 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

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. 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

11. 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

12. 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