Answer:
What is ASA Triangle Congruence?
ASA stands for “Angle, Side, Angle”, which means two triangles are congruent if they have an equal side contained between corresponding equal angles. If the vertices of two triangles are in one-to-one correspondence such that two angles and the included side of one triangle are congruent, respectively, to the two angles and the included side of the second triangles, then it satisfies the condition that the triangles are congruent. Because the two angles and the included side are equal in both the triangles, the triangles are called congruent.
What is AAS Triangle Congruence?
AAS stands for “Angle, Angle, Side”, which means two angles and an opposite side. AAS is one of the five ways to determine if two triangles are congruent. It 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 congruent to the corresponding angles and the non-included side of the second triangle, then the triangles are congruent. The non-include side is the side opposite to either one of the two angles being used. In simple terms, if two pairs of corresponding angles and the sides opposite to them are equal in both the triangles, the two triangles are congruent.
Difference between ASA and AAS
Terminology of ASA and AAS
– ASA and AAS are two postulates that help us determine if two triangles are congruent. ASA stands for “Angle, Side, Angle”, while AAS means “Angle, Angle, Side”. Two figures are congruent if they are of the same shape and size. In other words, two congruent figures are one and the same figure, in two different places. While both are the geometry terms used in proofs and they relate to the placement of angles and sides, the difference lies in when to use them. ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.
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.
Representation
– The main difference between the two congruence rules is that the side is included in the ASA postulate, whereas the side is not included in the AAS postulate.
