Triangle Congruence by ASA and AAS
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 Postulate
ASA = angle-side-angle
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...
If...
- ∠A ≅ ∠D
- AC ≅ DF
- ∠C ≅ ∠F
Then...
Then...
- ΔABC ≅ ΔDEF
AAS Postulate
AAS Postulate
AAS = angle-angle-side
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...
If...
- ∠A ≅ ∠D
- ∠C ≅ ∠F
- BC ≅ EF
Then...
Then...
- ΔABC ≅ ΔDEF