ASA and AAS Congruence Rule
The key difference between ASA and AAS congruence rule is listed as follows:
| Criteria | ASA Congruence Rule | AAS Congruence Rule |
|---|---|---|
| Components | Two angles and sides between them | Any two angles and any one side. |
|
Sequence |
The congruent elements must follow an angle-side-angle sequence in both triangles. |
Sequence of angle and sides doesn’t matter. |
| Example |
Consider two right triangles, △ABC (right angle at B) and △DEF (right angle at E). Then,
⇒ △ABC ≅ △DEF (by ASA) |
Consider two triangles, △ABC and △DEF. Then,
⇒ △ABC ≅ △DEF (by AAS) |
Note: If two angles of a triangle are equal, then, by the angle sum property of a triangle, we can easily conclude that the third angle is also equal. Thus, if any triangle is proven to be congruent by the ASA criterion, it can also be easily proved by the AAS criterion.
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ASA Congruence Rule | Definition, Proof & Examples
ASA Congruence Rule: ASA stands for Angle-Side-Angle. It is one of the congruence tests used to test the congruence of two triangles. Other than ASA there are 4 more congruence rules i.e., SSS, SAS, AAS, and RHS.
Condition of Congruency of Two Triangles: Two triangles are said to be congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
In this article, we will learn about the ASA Congruence Rule including its proof, applications, and examples related to it.
Table of Content
- What is Congruence?
- What is ASA Congruence Rule?
- Criteria for ASA Congruence Rule
- Proof of ASA Congruence Rule
- ASA and AAS Congruence Rule
- ASA Congruence Rule Class 9
- ASA Congruence Rule Solved Examples
- ASA Congruence Rule: Practice Problems