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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 = 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...

AB ≅ DE
BC ≅ EF
AC ≅ DF

Then...

ΔABC ≅ ΔDEF

Example

Given:

AC ≅ DB
AB ≅ DC

Prove that ΔABC ≅ ΔDCB

Statement

AC ≅ DB
AB ≅ DC
BC ≅ BC
ΔABC ≅ ΔDCB

Reason

Given
Given
Identity Property (they're the same thing)
SSS Postulate

SAS Postulate

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...

AB ≅ DE
∠A ≅ ∠D
AC ≅ DF

Then...

ΔABC ≅ ΔDEF

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

Given:

AB ≅ CB ≅ EB ≅ DB

Prove ΔABE ≅ ΔDBC

Statement

AB ≅ CB
EB ≅ DB
∠B ≅ ∠B
ΔABE ≅ ΔDBC

Reason

Given
Given
Vertical Angles
SAS Postulate

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Keywords: SSS, side-side-side, SAS, side-angle-side, postulate, proof

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