1. Warmup In triangle ABC, answer the following questions:
What side is opposite angle A?
What angle is opposite side AB?
What angle is included between sides AC and BC?
What side is included between angles A and C?
What is another way to write angle C? B A C

2. How can we use AAS and HL to prove triangles congruent?
Agenda:
Review SSS, SAS, ASA
AAS and HL notes/practice
Quiz Tomorrow

3. Practice (from yesterday)
Textbook p. 245 #9 – 26
Textbook p. 254 #10 – 14, 16, 17, 19, 21

4. Determine what is missing in order to use the indicated reason

5. 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.

6. 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

7. AAS vs. ASA
AAS
ASA

8. Parts of a Right Triangle
hypotenuse
legs

9. 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.

10. 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

11. 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!

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

13. 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

14. 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

15. 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

16. Practice
Textbook p. 254 #15, 18, 25
Textbook p. 260 # 1-12,

17. State if the two triangles are congruent and state the reason (SSS, SAS, ASA, AAS, HL)1. 2. 4. 3.