Postulates of congruence concerning triangles: (Do not write on this packet):
How can one tell by looking if two triangles are congruent?
Definitions:
Included angle:
The angle situated between two indicated
sides of a triangle.
Included side:
The side situated between two indicated
angles of a triangle.
Included angle.
Included side
Hypotenuse:
The longest side of a right triangle.
Leg:
Any of the two sides of a right triangle other
than the hypotenuse.
hypotenuse
Leg
Leg
Postulates:
Side-side-side (SSS):
Side-angle-side (SAS):
Angle-Side-Angle (ASA):
Angle-Angle-Side (AAS):
B
B
F
F
A
A
C
ABC 
G
EFG by ASA
E
C G
E
ABC  EFG by AAS
Two angles and the non included side.
Two angles and the included side.
Hypotenuse-Leg (HL):
CPCTC:
Corresponding parts of congruent triangles
are congruent.
Once two triangles have been established as
congruent, it can be automatically concluded
that each corresponding part will be
congruent.
Examples:
Page 201 # 2 to 10 (all). Write in your binders.
Practice 1:
Decide whether you can use the SSS or SAS Postulate to prove the triangles congruent. If
so, write the congruence statement, and identify the postulate. If not, write not possible.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Draw a triangle. Label the vertices A, B, and C.
10. What angle is between
11. What sides include
12. What angles include
and
?
?
?
13. What side is included between
and
?
14. Developing Proof Supply the reasons in this proof.
Given:
Prove:
Statements
Reasons
1.
a. __?__
2.
b. __?__
3.
c. __?__
15. Write a proof.
Given:
Prove:
Practice 2:
Tell whether the ASA Postulate or the AAS Theorem can be applied directly to prove the
triangles congruent. If the triangles cannot be proved congruent, write not possible.
1.
2.
3.
4.
5.
6.
7.
8.
10. Write a two-column proof.
9.
11. Write a flow proof.
Given:
Given:
Prove:
Prove:
What else must you know to prove the triangles congruent for the reason shown?
12. ASA
13. AAS
Practice 3:
Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove each statement
true.
1.
2.
3. K  P
4.
5.
6.
7.
8.
9.
Practice 4:
Write a two-column proof.
1. Given:
2. Given:
Prove:
Prove:
and
are right angles,
Evaluation:
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1.
Are the triangles shown congruent? If so, select the appropriate postulate. If not,
select “not congruent.”
a. ASA
c. AAS
b. SAS
d. not congruent
2.
If the triangles shown are congruent, select the appropriate postulate. If they are not
congruent, select “not congruent.”
a. SAS
c. SSS
b. ASA
d. not congruent
3.
The triangles shown are overlapping. If they are congruent, select the appropriate
postulate. If they are not congruent, select “not congruent.”
a. AAA
c. ASA
b. AAS
d. not congruent
4.Which of the following is not a valid reason for proving triangles congruent?
a. SSS
c. ASA
b. AAA
d. HL
5.
Which of the methods can be used to prove the triangles congruent?
a. SAS
c. AAS
b. ASA
d. SSS
Home work:
Part 1:
Page 190 # 22 to 27 (all)
Part 2:
Page 197 # 1 to 4 (all).
Evaluation taken from investigating geometry online.