LESSON 4-2
TRIANGLE CONGRUENCE
BY SSS AND SAS
Objective: Prove two triangles are congruent
using the SSS and SAS Postulates.
Key Concepts
(NOTES…DNG page 75-76)
SSS (Side-Side-Side) Postulate
If the three sides of one triangle are congruent to the three
sides of another triangle, then the two triangles are
congruent.
Proving Triangles Congruent
XY
MY
Reflexive Property of Congruence
SSS Postulate
AY
(DNG page 75)
Key Concepts
SAS (Side-Angle-Side) Postulate
If two sides and an included angle of one triangle are congruent
to two sides and an included angle of another triangle, then the
two triangles are congruent.
Vocabulary…
(DNG page 76)
What other information do you need to prove ADC  BCD by SAS?
Reflexive Property of Congruence
ADC  BCD
X
SAS
From the information given, can you prove RSG  RSH? Explain.
X
Reflexive Property of Congruence
SAS
///
///
Practice 4-2
Triangle Congruence by SSS & SAS
Decide whether you can use the SSS or SAS Postulate to prove the triangles congruent. If so, write
the congruence statement, and identify the postulate. If not, write not possible.
X
not possible
not possible
ADB ≅ CDB by SAS
TUS ≅ XWV by SSS
not possible
DEC ≅ GHF by SAS
Practice 4-2
Triangle Congruence by SSS & SAS
Decide whether you can use the SSS or SAS Postulate to prove the triangles congruent. If so, write
the congruence statement, and identify the postulate. If not, write not possible.
not possible
X
PRN ≅ PRQ by SSS
MKL ≅ KMJ by SAS
Draw a triangle. Label the vertices A, B, and C.
B
BCA
AB and BC
A
B and A
AC
C
Practice 4-2
14. Developing Proof
Triangle Congruence by SSS & SAS
Supply the reasons in this proof.
X
Statements
Reasons
1.
1.
Given
2.
Reflexive Property of
2.
AC  CA
3. ABC ≅ CDA
3.
SAS Postulate
≅
Practice 4-2
Triangle Congruence by SSS & SAS
15. Write a proof.
Statements
Reasons
1.
1.
Given
2. DFE ≅ HFG
2.
Vertical s are
3. DFE ≅ HFG
3.
SAS Postulate
≅.
Do not forget to take your HOMEWORK assignment sheet!!!