1. Warm Up
m<L = 180
120 + m<L = 180
m<L = 60 1. 2. 3. 4. 5. 6.
7z + 6 = 90
7z= 84
z = 12
5y = 90
y = 18
60o 12 18 24
60o 24
AC =
AC = 24
(also, AC = LN)
LN = 2(18) – 12
LN = 24
m<C = m<L
m<C = 60

2. Marking Congruent Triangles
Thm. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
If two triangles are congruent, then their corresponding parts are congruent.

3. Angle-Side-Angle (ASA)
If two angles and the ______________ side of one triangle are _____________ to two angles and the ____________ side of a second triangle, then the two triangles are ________________.
included
congruent
included
congruent

4. Side-Angle-Side (SAS)
If two sides and the _____________ angle of one triangle are __________ to two sides and the included angle of a second triangle, then the two triangles are ____________
included
congruent
congruent

5. Side-Side-Side (SSS)
If 3 sides of one triangle are _____________ to three sides of a second triangle, then the two triangles are ________________.
congruent
congruent

6. Angle-Angle-Side (AAS)F A B C D
nonincluded
If two angles and a _____________________ side of one triangle are _______________ to two angles and the corresponding ____________________ side of a second triangle, then the two triangles are ________________.
congruent
nonincluded
congruent

7. Hypotenuse-Leg (HL)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent .

8. Does AAA work?

9. Does AAA work?
NO!

10. Does ASS work?
No!
There is no ASS in geometry!

11. Other that the “given” information, you can only mark three things.
Very Important
Other that the “given” information, you can only mark three things.
Shared Side (Overlapping Side)
or a Shared Angle
2. Vertical Angles
3. Alternate Interior Angles (only if lines parallel).

12. Shared Side
statement
reason

13. Vertical Angles
statement
reason

14. Alternate Interior Angles (only if lines parallel)
statement
reason

15. Decide whether the triangles are congruent. Explain your reasoning.
Yes,
SAS

16. Decide whether the triangles are congruent. Explain your reasoning.
Yes,
AAS

17. Decide whether the triangles are congruent. Explain your reasoning.
Yes,
SAS

18. Decide whether the triangles are congruent. Explain your reasoning.
No,
SSA doesn’t work!

19. Decide whether the triangles are congruent. Explain your reasoning.
Yes,
AAS

20. Ex. State the third congruence that must be given to prove ABC  DEF.
GIVEN: A  D, ____________
Use the AAS Congruence Theorem.