In geometry, AAS means angle angle side and is one of the congruence theorems among the 5 different theorems that prove the congruency of two triangles. Whereas the AAS congruence rule states that if two corresponding angles with a non-included side are equal to each other, the two triangles are equal to each other. ASA congruence rule states that if two corresponding angles along with one corresponding side (included in between the angles) are equal to each other, the two triangles are congruent. These two are triangle congruence theorems that help in proving if two triangles are congruent or not. AAS: Where two angles of any two triangles along with a side that is not included in between the angles, are equal to each other.ĪAS stands for angle angle side and ASA refers to angle side angle.ASA: Where two angles along with a side included in between the angles of any two triangles are equal to each other.SAS: Where two sides and an angle included in between the sides of two triangles are equal to each other.SSS: Where three sides of two triangles are equal to each other.The 4 different triangle congruence rules are: Whereas AAS deals with two angles with a side that is not included in between the two angles of any two given triangles. How Do You Tell if a Triangle is ASA or AAS?īoth the triangle congruence theorems deal with angles and sides but the difference between the two is ASA deals with two angles with a side included in between the angles of any two triangles. The Angle Angle Side Postulate (AAS) states that if two consecutive angles along with a non-included side of one triangle are congruent to the corresponding two consecutive angles and the non-included side of another triangle, then the two triangles are congruent. Corresponding Parts of Congruent TrianglesįAQs on AAS Congruence Rule What is AAS Congruence Rule?.Listed below are a few topics related to the AAS congruence rule, take a look. Therefore, according to the ASA congruence rule, it is proved that ∆ABC ≅ ∆DEF. Since we already know that ∠B =∠E and ∠C =∠F, so We also saw if two angles of two triangles are equal then the third angle of both the triangle is equal since the sum of angles is a constant of 180°. We know that AB = DE, ∠B =∠E, and ∠C =∠F. To prove the AAS congruence rule, let us consider the two triangles above ∆ABC and ∆DEF. We should also remember that if two angles of a triangle are equal to two angles of another, then their third angles are automatically equal since the sum of angles in any triangle must be a constant 180° (by the angle sum property). The AAS congruence rule states that if any two consecutive angles of a triangle along with a non-included side are equal to the corresponding consecutive angles and the non-included side of another triangle, the two triangles are said to be congruent. To prove the AAS congruence rule or theorem, we need to first look at the ASA congruence theorem which states that when two angles and the included side (the side between the two angles) of one triangle are (correspondingly) equal to two angles and the included side of another triangle.
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