Download Side - Harding Charter Preparatory High School

The 5 Congruence
Mathematical Tools
for High School Geometry
by Ms. C. Henry
SSS AND SAS CONGRUENCE POSTULATES
POSTULATE
POSTULATE 19 Side - Side - Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides
of a second triangle, then the two triangles are congruent.
If Side
S MN
QR
Side
S NP
RS
Side
S PM
SQ
then  MNP
 QRS
SSS AND SAS CONGRUENCE POSTULATES
POSTULATE
POSTULATE 20 Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of a
second triangle, then the two triangles are congruent.
If
Side
S
Angle
A
Side
S
PQ
WX
Q
X
QS
XY
then  PQS
WXY
ASA AND AAS CONGRUENCE
POSTULATE
POSTULATE 21 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
SSide
Angle
A
Q
X
RQ
YX
R
Y
then  RPQ
R
 YZX
P
Z
Q
4.4
Proving Triangles are Congruent: ASA and AAS
X
Y
ASA AND AAS CONGRUENCE
THEOREM
THEOREM 4.5 Angle- Angle- Side (AAS) Congruence Theorem
If two angles and a non-included side of one triangle are
congruent to two angles and the corresponding non-included
side of a second triangle, then the two triangles are congruent.
If
A
M
Q
N
A
S NP
Side
R
then  MNP
RS
N
M
4.4
 QRS
R
P
Q
Proving Triangles are Congruent: ASA and AAS
S
HL CONGRUENCE
THEOREM
THEOREM 4.8 Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to
the hypotenuse and a leg of a second triangle, then the two
triangles are congruent.
If Side
H MN
QR
Side
L NP
RS
then  MNP
M
P
4.6
 QRS
Q
N
S
Proving Triangles are Congruent: HL (Hypotenuse-Leg)
R
Remember!!!
There is no congruence for:
 SSA
 AAA