#### Transcript Triangle Congruence by SSS and SAS

```Triangle Congruence:
by SSS and SAS
Geometry (Holt 4-5)
K. Santos
Side-Side-Side (SSS)
Congruence Postulate (4-5-1)
If the three sides of one triangle are congruent to the three
sides of another triangle , then the two triangles are
congruent.
A
D
Given: π΄πΆ β π·πΈ
π΅πΆ β πΉπΈ
E
π΄π΅ β π·πΉ
B
C
F
Then: β π΄π΅πΆ β βπ·πΉπΈ
Included Angle
Included angleβis an angle formed by two adjacent sides.
A
B
C
< B is the included angle between sides π΄π΅and π΅πΆ
Side-Angle-Side (SAS)
Congruence Postulate (4-5-2)
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another
triangle, then the two triangles are congruent.
Given: π΄π΅ β πΎπΏ
π΄πΆ β πΎπ½
< A β< K
A
B
J
C
K
L
Then: β π΄π΅πΆ β βπΎπΏπ½
Please note both angles must be included between the sides!!!
ExampleβWriting a
congruence statement
Write a congruence statement for the congruent triangles and
name the postulate you used to know the triangles were
congruent.
1. D
F
R
E
T
βπ·πΈπΉ β β πππ
S
2.
A
B
C
SAS Postulate
SSS Postulate
D
Exampleβwhat other
information is needed
What other information do you need to prove the two triangles
congruent by SSS or SAS?
1. M
T
2. G
H
U
N
O
V
Q
R
I
S
Need <M β <U for SAS
or need ππ β ππ for SSS
need <G β <Q for SAS
or need πΌπ» β ππ for SSS
Exampleβexplain triangle
congruence
Use the SSS or SAS postulate to explain why the triangles are
congruent.
A
B
D
C
It is given: π΄π΅ β πΆπ· and π΄π· β πΆπ΅
You know: π΄πΆ β πΆπ΄ by reflexive property of congruence
So: βADC β βCBA by SSS Postulate
Exampleβverifying triangle
congruence
Show that the triangles are congruent for the given value of the
variable. βUVW β βYXZ, a = 3
U
X
4
V
ZY = a β 1
ZY = 3 β 1
ZY = 2
ππ β ππ
2
W
3
So, βUVW β βYXZ
a
3a - 5
Z aβ1
XZ = a
XZ =3
ππ β ππ
Y
XY = 3a - 5
XY = 3(3) - 5
XY = 4
ππ β ππ
Proof
Q
Given: ππ bisects <RQS
ππ β ππ
Prove: βRQP β βSQP
P
R
Statements
1.
2.
3.
4.
ππ bisects <RQS
< RQP β < SQP
ππ β ππ
ππ β ππ
5. βRQP β βSQP
1.
2.
3.
4.
S
Reasons
Given
Definition of angle bisector
Given
Reflexive property of
congruence
5. SAS Postulate (3, 2, 4)
Proof
πΈπΊ || π»πΉ
πΈπΊ β π»πΉ
Prove: βUVW β βYXZ
Given:
E
G
F
Statements
1. πΈπΊ || π»πΉ
2. < EGF β <HFG
1.
2.
3. πΈπΊ β π»πΉ
4. πΉπΊ β πΊπΉ
3.
4.
5. βUVW β βYXZ
5.
H
Reasons
Given
Alternate Interior Angles
Theorem
Given
Reflexive Property of
congruence
SSS Postulate (2, 3, 4)
```