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CHAPTER 4 DOMINOES
If the sides of one triangle are congruent to the sides of a second triangle, then the
triangles are congruent.
P. 206
SSS Postulate
AC  DF
F
C
AB  DE
ABC

DEF
A
BC  EF
B
D
E
If two sides and the included angle of one triangle are congruent to two sides and the
included angle of another triangle, then the triangles are congruent.
P. 207
SAS Postulate
AC  DF
BC  EF
F
C
ABC

DEF
C  F
A
B
D
E
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.
P. 207
ASA Postulate
A  D
B  E
C
ABC

F
DEF
AB  DE
A
B
D
E
If two angles and a nonincluded side of one triangle are congruent to the corresponding two
angles and side of a second triangle, then the triangles are congruent.
P. 214
AAS Theorem (4-5)
A  D
B  E
AC  DF
Chapter 4 Theorem Dominoes, page 1
F
C
ABC

DEF
A
B
D
E
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
P. 222
Isosceles Triangle
Theorem (4-6) and
(4-7)
B
AB  BC
A  C
C
A
If two angles of a triangle are congruent, then the sides opposite those angles are
congruent.
If a triangle is equilateral, then it is equiangular.
P. 224
Corollary 4-3
B
AB  BC  AC
ABC is
equiangular
C
A
If a triangle is equilateral, then each angle measures 60°.
P. 224
Corollary 4-3
ABC is equilateral.
Chapter 4 Theorem Dominoes, page 2
mA = 60°
mB = 60°
mC = 60°
B
60°
A
60° 60°
C
If a triangle is a right triangle, then one angle is a right angle.
P. 180
Definition of Right
Triangle
B
ABC is a right
triangle.
BCA is a right
angle
C
A
If the legs of one right triangle are congruent to the corresponding legs of another right
triangle, then the triangles are congruent.
P. 245
Theorem 5-5 (LL)
DEF and
RST
are right triangles
EF  ST
D
DEF

R
RST
E
ED  SR
F S
T
If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse
and corresponding acute angle of another right triangle, then the two triangles are
congruent.
P. 246
Theorem 5-6 (HA)
DEF and
RST
are right triangles
DF  RT
EDF  SRT
D
DEF

R
RST
E
F S
T
If one leg and an acute angle of one right triangle are congruent to the corresponding leg
and acute angle of another right triangle, then the triangles are congruent.
P. 247
Theorem 5-7 (LA)
DEF and
RST
are right triangles
ED  SR
DFE  RTS
D
DEF

R
RST
E
F S
T
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.
P. 247 Postulate 5-3
(HL)
DEF and
RST
are right triangles
DF  RT
EF  ST
Chapter 4 Theorem Dominoes, page 3
D
DEF

R
RST
E
F S
T