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DifferencesMathematics

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The study of geometry is enjoyable. Sizes, distances, and angles are the primary focus of this branch of mathematics known as geometry. Shapes are the focus of geometry, a branch of mathematics. It's not hard to understand how geometry may be used to solve problems in the actual world. It finds application in a wide range of fields, including engineering, architecture, the arts, sports, and more.

Today, we'll talk about a special topic in triangle geometry called **congruence**. But first, let's define congruence so we may use it. Whenever one figure can be superimposed over the other in such a way that all of its elements match up, we say that the two figures are congruent. That is, if two figures share the same dimensions and shape, we say that they are congruent. If you take a look at two congruent figures, you'll see that they are the same shape at two distinct locations.

True, triangle congruence serves as the cornerstone of many geometrical theorems and proofs. The notion of triangle congruence is central to the study of geometry in high school. The idea of sufficiency, that is, determining the criteria which fulfil that two triangles are congruent, is often disregarded while teaching and learning about triangle congruence.

We will just cover two of the five possible methods for checking congruence between two triangles (the ASA and AAS methods). To clarify, "Angle, Angle, Side" (AAS) is the opposite of "Angle, Side, Angle" (ASA). Let's check out how you may utilise the two to figure out if a pair of triangles is indeed congruent.

## ASA Triangle Congruence

ASA stands for Angle-Side-Angle. This criterion states that 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. In other words, if we know that two triangles have two angles and one side in common, then we can conclude that they are congruent.

## AAS Triangle Congruence

AAS stands for Angle-Angle-Side. This criterion states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent. In other words, if we know that two triangles have two angles and one non-included side in common, then we can conclude that they are congruent.

## Differences: ASA and AAS

The main difference between ASA and AAS is the order in which the angles and sides are congruent. In ASA, the included side is between the two congruent angles, while in AAS, the non-included side is opposite to one of the congruent angles. This means that in ASA, we have two angles and one side, while in AAS, we have two angles and two sides.

Another difference between ASA and AAS is the number of sides that are congruent. In ASA, we only have one side that is congruent, while in AAS, we have two sides that are congruent. This means that AAS is a stronger criterion than ASA, as it requires more information to prove congruence.

## When to Use ASA and AAS?

ASA and AAS criteria are used to prove congruence between two triangles. However, they are not interchangeable, and it is important to use the correct criterion for the given situation.

ASA criterion is used when we have two angles and the included side in common. This is useful in situations where we are given the length of one side and two angles, and we need to find the length of another side.

AAS criterion is used when we have two angles and one non-included side in common. This is useful in situations where we are given the length of two sides and one angle, and we need to find the length of another side.

The following table highlights the major differences between ASA and AAS Triangle Congruence −

Characteristics | ASA | AAS |
---|---|---|

Terminology | ASA stands for “Angle, Side, Angle”. ASA refers to any two angles and the included side. | AAS means “Angle, Angle, Side”. AAS refers to the two corresponding angles and the non-included side./p> |

Congruence | According to ASA congruence, two triangles are congruent if they have an equal side contained between corresponding equal angles. In other words, if two angles and an included side of one triangle are equal to the corresponding angles and the included side of the second triangle, then the two triangles are called congruent, according to the ASA rule. | The AAS rule, on the other hand, states that if the vertices of two triangles are in one-to-one correspondence such that two angles and the side opposite to one of them in one triangle are equal to the corresponding angles and the non- included side of the second triangle, then the triangles are congruent. |

## Conclusion

In summary, ASA and AAS are two criteria used in geometry to determine when two triangles are congruent. ASA requires two angles and the included side to be congruent, while AAS requires two angles and one non-included side to be congruent. It is important to use the correct criterion for the given situation to prove congruence between two triangles.

Vineet Nanda

Updated on: 17-Apr-2023

3K+ Views

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