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4.3 Congruent
Triangles
Congruence Theorem
SSS
If the sides of one triangle are
congruent to the sides of a second
triangle, then the triangles are
congruent.
A
B
D
C E
F
Vocabulary
Included Angle: In a triangle, the angle
formed by two sides is the included angle
for the two sides.
Included Side: The side of a triangle that
forms a side of two given angles.
Included Angles &
Sides
Included Angle:
A is the included angle for AB & AC.
A
B is the included angle for BA & BC.
*
C is the included angle for CA & CB.
Included Side:
B
AB is the included side for A & B.
BC is the included side for B & C.
AC is the included side for A & C.
*
*
C
Congruence Theorems
ASA If two angles and the included side of one triangle are
congruent to the two angles and the included side of another
triangle, then the triangles are congruent.
A
B
SAS
A
D
C
E
F
B
D
C
E
F
If two sides and the included angle of one triangle are
congruent to the two sides and the included angle of another
triangle, then the triangles are congruent.
Congruence Theorems
AAS If two angles and a non included side of one triangle are
congruent to the corresponding two angles and side of a
second triangle, then the two triangles are congruent.
A
B
HL
C
E
D
A
D
F
B
C
E
If the hypotenuse and a leg of one right triangle are
congruent to the hypotenuse and corresponding leg of
another right triangle, then the triangles are congruent.
F
Are these triangles congruent? If so, why
and name the triangles.
B
A
E
C
F
D
S
B
A
C
R
T
S
B
A
C
R
T
S
B
A
C
R
T
S
B
A
C
R
T
You can only use what is marked in the picture! You can
not mark anything else in the pictures EXCEPT:
1. Vertical angles
2. Shared side (by the reflexive property,
any side is congruent to itself).
3. If there are parallel lines, you can mark
alternate interior angles (they make a Z
shape).
Name the congruent triangles.
A
C
B
E
D
Name the congruent triangles.
X
W
Y
Z
Name the congruent triangles.
A
D
B
C