1. Sections
Triangle Congruence

3. Example 1: ∆FGJ  ∆HGJ by SSS
Assume that G is the midpoint of Explain whether or not ∆FGJ and ∆HGJ are congruent.
∆FGJ  ∆HGJ by SSS

4.  Not  by SSS On Your Own 1: by SSS
Decide whether or not the congruent statement is true. Explain your reasoning.
a b. 
by SSS
Not  by SSS

6. Example 2:
Use the diagram to name the included angle between the given pair of sides.
a. b. c.
HGI
HIG H

7. On Your Own 2:
Use the diagram to name the included angle between the given pair of sides.
a. b. c. J
HGI
GIJ

10. congruent
Leg:
Hypotenuse:
2 shorter sides of a right triangle
Longest side of a right triangle and opposite the right angle

13. Example 3a
Decide whether enough information is given to prove that the triangles are congruent by using SAS.

14. Example 3b
Decide whether enough information is given to prove that the triangles are congruent by using SAS.
Not enough info

15. Example 4:
Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem.
B) B and  D are both right angles.
C is the midpoint of A)

16. On Your Own 4:
Decide whether there is enough information to prove that the two triangles are congruent by using HL theorem.
c d.

17. Example 5: Identify congruent triangles
Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.
a. b. c.
Yes AAS
NO AAA
Yes ASA

18. On Your Own 5:
Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.
c. TSW  WVT? d.
Yes ASA NO

19. Combining All the Congruence Theorem Postulates
Are the 2 triangles congruent?

20. AAS congruence theorem
Nope, AAA does not insure that triangles congruent
AAS congruence theorem

21. ASA congruence theorem
Reflexive Property
HL congruence theorem

22. AAS congruence theoremf) D B F E C A

23. No theorem to prove the 2 triangles congruent
SSS congruence theorem h)
Reflexive Property

24. SAS congruence theoremi)
Reflexive Property

25. Decide whether enough information is given to prove that the triangles are congruent (STATE THE CONGRUENCE THEOREM!)
j k.
SSS
SAS

26. Decide whether enough information is given to prove that the triangles are congruent (STATE THE CONGRUENCE THEOREM!)
l m. NO NO

27. EXTRA PRACTICE
Explain how you can prove that the indicated triangles are congruent using the given postulate or theorem. a. b. c.

28. Practice problems
State the third congruence that is needed to prove that ∆ DEF ∆ ABC, using the given postulate or theorem. 1. 2. 3.
 E   B

29. Tell whether you can use the given information to show that ∆ JKL  ∆ RST.4. 5. 6. 7. NO
Yes AAS
Yes ASA NO