Proving Triangles Congruent SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem.
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Transcript of Proving Triangles Congruent SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem.
Proving Triangles Congruent
SSS Postulate, SAS Postulate
ASA Postulate, AAS Theorem
& HL Theorem
Side - Side - Side Postulate
• If three sides of one triangle are congruent to three sides of another triangle, then
• the two triangles are congruent.
• ABC DEF
A C
B
F
E
D
SSS Example:
E
T
I
K
ITK
ETK
Side - Angle - Side Postulate
• If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then
• the two triangles are • JKL MNO
O
N
M
J L
K
SAS Example
ARK ?
ERN
K N
E
R
A
Angle - Side - Angle Postulate
• If two angles and the included side of one triangle are to two angles and the included side of another triangle, then
• the triangles are • PQR STU
U
T
S
R Q
P
ASA Example
MY
R
A
AY Bisects < MAR
YMA ?
YRA
Angle - Angle - Side Theorem• If two angles and a
nonincluded side of one triangle are to two angles and the corresponding nonincluded side, then
• the triangles are • XYZ JAC
C
J A
Z
Y X
AAS Example
K Y
RE
RKY ? KRE
Hypotenuse-Leg Theorem• If the hypotenuse
and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then
• the triangles are • RPW SBM
R
P W
S
B M
QMC ?
QHC
Q
HC
M
HL Example
Example 1
ME
K
I
IEM ? IEK
Property?
SAS
Example 2
RBA ? IBT
Property?
ASA
R
T
IB
A
Example 3
MOU ?None
Property?None: SSA
isn’t a property
M
E
SU
O
Example 4
RIK ? SKI
Property?
SSS
K
S
I
R
Example 5
SIL ?
LAS
Property?
AAS
L A
SI
RBI ? GBI
Property?
HLI
R GB
Example 6
MISSING PARTS
What information do you need to prove the following triangles are congruent by SAS?
Q
W
E
RT
RWQW
MISSING PARTS
What information do you need to prove the following triangles are congruent by ASA?
FDGADS
A S
D F
G
63o
63o
MISSING PARTS
What information do you need to prove the following triangles are congruent by AAS?
YUIITY
T Y
UI
MISSING PARTS
What information do you need to prove the following triangles are congruent by SSS?
VCYB
Y
C
V
B
6
6
MISSING PARTS
What information do you need to prove the following triangles are congruent by HL?
HQMQ
HCMC
OR
Q
HC
M