Triangle Congruence by SSS and SAS
Triangle Congruence by SSS and SAS
Standard
G.SRT.5 Use congruence... criteria for triangles to solve problems and to prove relationships in geometric figures.
SSS Postulate
SSS Postulate
SSS = side-side-side
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.
If...
If...
- AB ≅ DE
- BC ≅ EF
- AC ≅ DF
Then...
Then...
- ΔABC ≅ ΔDEF
Example
Example
Given:
- AC ≅ DB
- AB ≅ DC
Prove that ΔABC ≅ ΔDCB
Statement
Statement
- AC ≅ DB
- AB ≅ DC
- BC ≅ BC
- ΔABC ≅ ΔDCB
Reason
Reason
- Given
- Given
- Identity Property (they're the same thing)
- SSS Postulate
SAS Postulate
SAS Postulate
SAS = side-angle-side
SAS = side-angle-side
Postulate:
- 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.
If...
If...
- AB ≅ DE
- ∠A ≅ ∠D
- AC ≅ DF
Then...
Then...
- ΔABC ≅ ΔDEF
Tip for recognizing SAS
Tip for recognizing SAS
- The angle must be in between the two sides! Just like how it is written, side-angle-side. The angle is in between.
Example
Example
Given:
- AB ≅ CB ≅ EB ≅ DB
Prove ΔABE ≅ ΔDBC
Statement
Statement
- AB ≅ CB
- EB ≅ DB
- ∠B ≅ ∠B
- ΔABE ≅ ΔDBC
Reason
Reason
- Given
- Given
- Vertical Angles
- SAS Postulate
Keywords: SSS, side-side-side, SAS, side-angle-side, postulate, proof