Download Proving Triangles Congruent

Proving Triangles
Congruent
Part 2
AAS Theorem
If two angles and one of the nonincluded sides in one triangle are
congruent to two angles and one of
the non-included sides in another
triangle, then the triangles are
congruent.
AAS Looks Like…
A
B
G
F
C
A: K  M
A: KJL  MJL
S: JL  JL
JKL  JML
J
D
A: A  D
A: B  G
S: AC  DF
ACB  DFG
K
L
M
AAS vs. ASA
AAS
ASA
Parts of a Right Triangle
hypotenuse
legs
HL Theorem
RIGHT TRIANGLES ONLY!
If the hypotenuse and one leg of a
right triangle are congruent to the
hypotenuse and leg of another
right triangle, then the triangles
are congruent.
HL Looks Like…
M
W
N
T
V
Right : M & Q
H: PN  RS
R L: MP  QS
NMP  RQS
P
Right : TVW & XVW
H: TW  XW
L: WV  WV
WTV  WXV
Q
S
X
There’s no such thing as AAA
AAA Congruence:
These two equiangular triangles have all the
same angles… but they are not the same size!
Recap:
There are 5 ways to prove that triangles
are congruent:
SSS
SAS
ASA
AAS
HL
Examples
D
M
N
L
A
C
B
B is the midpoint of AC
S: AB  BC
A: ABD  CBD
S: DB  DB
SAS ABD  CBD
A: L  J
A: M  H
S: LN  JK
H
J
AAS
K
MLN  HJK
Examples
C
B
B
A
C
E
D
A
A: A  C
S: AE  CE
A: BEA  DEC
ASA
BEA  DEC
D
DB ^ AC
AD  CD
HL
ABD  CBD
Right Angles: ABD & CBD
H: AD  CD
L: BD  BD
Examples
A
W
B
D
B is the midpoint of AC
SSS
DAB  DCB
S: AB  CB
S: BD  BD
S: AD  CD
C
Z
X
V
A: WXV  YXZ
S: WV  YZ
Y
Not Enough!
We cannot conclude
whether the triangle
are congruent.