Download 4.4 Proving Triangles are Congruent: ASA and AAS

NOTES 3.8 & 7.2
Triangle Congruence
HL and AAS
SSS (Side-Side-Side) Postulate
 If 3 sides of one triangle are congruent to 3 sides of another
triangle, then the triangles are congruent.
A
B
Y
C
ABC ≅
X
Z
XYZ
SAS (Side-Angle-Side)
Postulate
If 2 sides and the included angle of one triangle are
congruent to 2 sides and the included angle of
another triangle, then the triangles are congruent.
A
Y
B
C
ABC ≅
Z
XYZ
X
ASA (Angle-Side-Angle) 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 triangles are
congruent.
B
A
E
C
F
D
AAS (Angle-Angle-Side) Theorem
• If two angles and a
non-included side of
one triangle are
congruent to two
angles and the
corresponding nonincluded side of a
second triangle, then
the triangles are
congruent.
B
A
E
C
F
D
IMPOSSIBLE METHODS:
Angle-Side-Side or Angle-Angle-Angle
ASS or SSA – can’t spell bad word
AAA – proves similar , not congruent
.
A
Y
B
C
ABC ≅
Z
XYZ
X
HL (Hypotenuse - Leg) Theorem:
• If the hypotenuse and a leg of a right triangle are congruent to the
hypotenuse and leg of a second right triangle, then the two triangles are
congruent.
• Example:
because of HL.
ABC  XYZ
A
X
B
C
Y
Z
Triangles are congruent by…
SSS
AAS
SAS
ASA
HL
Theorem 53
• If 2 angles of one triangle are congruent to 2 angles of another
triangle, then the 3rd angles must be congruent.
• AKA – No Choice Theorem
• Triangles do not have to be congruent for this theorem.