Lesson 5.3 Proving Triangles are
Congruent: ASA and AAS
Pages 250 - 252
Angle-Side-Angle Congruence
Postulate (ASA)
If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, then the
triangles are congruent.
M
B
Angle– B ≅ M
A
Side – BO ≅ MA
O
W
Angle– O ≅ A
Therefore, by ASA, BOW ≅ MAN
N
Does the diagram show that the triangles
are congruent by ASA?
N
P
O
M
L
K
Angle-Angle-Side Congruence
Postulate (AAS)
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 triangles are congruent.
M
B
Angle – B ≅ M
Angle - O ≅ A
O
Side – BW ≅ MN
Therefore, by AAS, BOW ≅ MAN
A
W
N
Does the diagram give enough information
to use the AAS Congruence Postulate?
A
L
H
T
S
R
R
P
Writing Proofs
A proof is a convincing argument that
shows why a statement is true. A twocolumn proof has numbered statements
and reasons that show the logical order
of the argument. Each statement has a
reason listed to its right.
How to Write a Proof
•
•
•
•
List the given information first
Use the information from the diagram
Give a reason for every statement
Use given information, definitions, postulates,
and theorems as the “Reasons”
• List statements in order.
• End the proof with the statement that you are
trying to prove.
Write a 2-Column Proof that shows
JKL ≅ NML
Given: JK ≅ MN and J ≅ N
Prove: JKL ≅ NML
J
Statements:
Reasons:
1.
1.
2.
2.
K
3.
3.
4.
4.
M
L
N
Write a 2-Column Proof that shows
DRA ≅ DRG
Given: A ≅ G, R ≅ R, R is the midpoint of AG
D
Prove: DRA ≅ DRG
Statements:
Reasons:
1.
1.
2.
2.
R
G
A
3.
3.
4.
4.
5.
5.
.
Assignment:
Pages 254 – 256
#14 – 26 even, #34, #38 – 44 even
and
5.3 Practice B worksheet