Geometry G.6 (4.5 4.6) ASA, AAS, Use Congruent Triangles NOTES
Ms. Graham/Mrs. Fonte
Name: _______________________________ Date: _____________ Block: _______
Prove Triangles Congruent by ASA and AAS
Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are
congruent to two angles and the included side of a second
triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem
If two angles and a non-included side of one triangle are
congruent to two angles and the corresponding non-included
side of a second triangle, then the two triangles are congruent.
Examples: 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)
Congruent? ______
Why or why not?______
Congruent? ______
Why or why not?______
Congruent? ______
Why or why not?______
d)
e)
f)
Congruent? ______
Why or why not?______
Congruent? ______
Why or why not?______
Congruent? ______
Why or why not?______
Example Proofs:
Given:  PQS   RQS
Given:  KLN   MNL
 QSP   QSR
KN || ML
Prove: ∆PQS  ∆RQS
Prove: ∆KLN  ∆MNL
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Geometry G.6 (4.5 4.6) ASA, AAS, Use Congruent Triangles NOTES
Ms. Graham/Mrs. Fonte
Use Congruent Triangles to Prove Corresponding Parts Congruent

CPCTC can be used to prove corresponding parts of congruent triangles congruent
Examples:
a)
Explain how you would use the
given information and
congruent triangles to prove
the statement.
Given: AB || DE , AB  DE
b)
Explain how you would use the
given information and congruent
triangles to prove the
statement.
Prove: JK  LK
Prove: C is the midpoint of BE

What triangles need to be  ? ________

What triangles need to be  ? _________

Can they be proven  ? How?_________

Can they be proven  ? How?_________

Can we reach our conclusion? Why?_____

Can we reach our conclusion? Why?_____
c) Plan a proof:
Given: 1  2 , 3  4
Prove: ∆DEF  ∆DCB

d) Plan a proof:
Given:
AB  EB , FB  CB
What do we know, and
what do we need to
prove ∆DEF  ∆DCB ?

Can we prove EDF  CDB ? How? _____

What triangles need to be  to show
ED  CD ?________ Can we? How? _____

What can we conclude about ED  CD ?
Why? ___________________

Can we now conclude ∆DEF  ∆DCB?
Why?________________________
Prove: BG  BD
Plan:

What triangles can be proved  ? _______

How will you prove it?_______

Is this enough, or other ∆s need to be  ?
Which triangles? ___________

How will you prove them  ?_________

Can we conclude BG  BD ? Why?________
You try:
a) Plan a proof given
the information in
the diagram.
Prove: RPQ  TRS
b) Write a proof given
the information in the
diagram.
Prove: DB  CB
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