Triangle Congruence by ASA and AAS

Standard

G.SRT.5 Use congruence... criteria for triangles to solve problems and to prove relationships in geometric figures.

ASA Postulate

ASA = angle-side-angle

Postulate:

  • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
  • Included side means the side in between the two angles.

If...

  • ∠A ≅ ∠D
  • AC ≅ DF
  • ∠C ≅ ∠F

Then...

  • ΔABC ≅ ΔDEF

AAS Postulate

AAS = angle-angle-side

Postulate:

  • If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
  • Nonincluded means that the side is not in between the two angles.

If...

  • ∠A ≅ ∠D
  • ∠C ≅ ∠F
  • BC ≅ EF

Then...

  • ΔABC ≅ ΔDEF