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

  1. AC ≅ DB
  2. AB ≅ DC
  3. BC ≅ BC
  4. ΔABC ≅ ΔDCB

Reason

  1. Given
  2. Given
  3. Identity Property (they're the same thing)
  4. 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

  1. AB ≅ CB
  2. EB ≅ DB
  3. ∠B ≅ ∠B
  4. ΔABE ≅ ΔDBC

Reason

  1. Given
  2. Given
  3. Vertical Angles
  4. SAS Postulate
Keywords: SSS, side-side-side, SAS, side-angle-side, postulate, proof