Transcript 4.5 – Prove Triangles Congruent by ASA and AAS

4.5 – Prove Triangles
Congruent by ASA and AAS
Geometry
Ms. Rinaldi
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.
If Angle A  R
Side CA  TR
Angle C  T
Then
ABC  RST
B
C
A
S
T
R
EXAMPLE 1
Use ASA
Decide whether the congruence
statement is true.
Explain your reasoning.
ABC  JKL
SOLUTION
(A)
B  K
(S)
BA  KJ
(A)
A  J
So, by ASA,
ABC  JKL
EXAMPLE 2
Use ASA
Decide whether the congruence
statement is true.
Explain your reasoning.
LMN  PON
Angle-Angle-Side (AAS)
Congruence Postulate
If two angles and the non-included
side of one triangle are congruent to
two angles and the non-included
side of a second triangle, then the
two triangles are congruent.
If Angle A  R
Angle C  T
Side
BC  ST
Then ABC  RST
B
C
A
S
T
R
EXAMPLE 3
Use AAS
Decide whether the congruence
statement is true.
Explain your reasoning.
RST  TUR
SOLUTION
U  S
(A) URT  STR
(A)
(S) RT  RT
So, by AAS,
RST  TUR
EXAMPLE 4
Use AAS
Decide whether the congruence
statement is true.
Explain your reasoning.
HDE  FGE
EXAMPLE 5
Use ASA or AAS
State the third congruence that must be given to prove that
ABC  DEF using the indicated postulate.
B
Given:
A  D
E
AB  DE
Use the ASA Congruence Postulate.
C
A
D
F
EXAMPLE 6
Use ASA or AAS
State the third congruence that must be given to prove that
ABC  DEF using the indicated postulate.
B
Given:
C  F
E
 B  E
Use the ASA Congruence Postulate.
C
A
D
F
EXAMPLE 7
Use ASA or AAS
State the third congruence that must be given to prove that
ABC  DEF using the indicated postulate.
B
Given:
A  D
E
C  F
Use the AAS Congruence Postulate.
C
A
D
F