What is ASA?
ASA is a condition of congruency. Full form of ASA is angle-side-angle. Under this condition of congruency two triangles should have two angles and corresponding side between angles equal. Formula of ASA is A=B-C. This condition is easier than other conditions.
ASA is a narrower condition. It cannot be used in proving similarity. ASA can only be used in geometry and not in trigonometry. ASA can be used to determine degree of similarity but not to prove similarity. Range of angle under this condition is 0° to 180°. For using this condition to prove two triangles congruent, it is important to know measurement of side and degree of angle.
For example: Two triangles ABC and PQR are said to be congruent under the condition ASA is when corresponding angles and a side between the angles in both the triangles are equal i.e <A=<P , AB=PQ and <B=<Q.
What is AAS?
AAS is a condition used to prove congruency and similarity of a triangle. AAS stands for angle-angle-side. Under this condition two triangles are said to be congruent if corresponding angles and any corresponding side are equal. It is not necessary that side between the angles are included in this condition. Formula of AAS is C=A-B This condition is comparatively difficult that other conditions.
AAS is a broader condition. It can be used to prove triangles similar as well. AAS can also be used in trigonometry along with geometry. Range of angle under AAS is 0° to 360°. For using this condition to prove two triangles congruent, it is important to know degree of angles of a triangle.
For example: Two triangles ABC and PQR are said to be congruent under the condition AAS is when corresponding angle and any one side in the both the triangles are equal i.e <A=<P , <B=<Q and AB=PQ/AC=PR.
Two triangles ABC and PQR are said to be similar under the condition AA is when any two angles of the triangle is equal.
Difference Between ASA and AAS
- ASA means angle-side-angle. While AAS means angle-angle-side.
- ASA is the condition where the side taken must be between the two angles taken. AAS is the condition where the side taken does not need to be between angles taken.
- ASA is a easier way to prove two triangles congruent. While AAS is comparatively difficult way.
- ASA includes range of angle 0° to 180°. While AAS includes angle of range 0° to 360°.
- ASA cannot be used to prove similarity. While AAS is used to prove similarity.
Comparison Between ASA and AAS
| Parameters of Comparison | ASA | AAS |
| Full-form | Angle-Side-Angle | Angle-Angle-Side |
| Definition | It is defined as angles between two side of triangle | It is defined as any two angles and any other side of triangle |
| Side | Side is between the angles are included | Any side can be included |
| Difficulty | Easy to prove | Comparatively difficult |
| Used for | Proving congruency but not similarity | Proving congruency and similarity |
| Range of angles | 0° to 180° | 0° to 360° |
| Example | For proving congruency in triangle LMN and OPQ <L = <O , LM=OP and <M=<P | Triangles LMN and OPQ are congruent if <L=<O , <N=<Q and LM = OP |