Before learning the SAS triangle formula let us recall what is congruence and similarity. Congruence of triangles means that all corresponding angle pairs are equal and all corresponding sides are equal. If two triangles are similar, it means that all corresponding angle pairs are equal and all corresponding sides are proportional. However, in order to be sure that the two triangles are similar or congruent, we do not necessarily need to have information about all sides and all angles. Using SAS Triangle Formula, congruency or similarity of any two triangles can be checked when two sides and the angle between these sides for both the triangles follow the required criterion. Let us understand the desired criterion using the SAS triangle formula using solved examples in the following sections.
What Is SAS Triangle Formula?
There are different SAS Triangle formulas used to prove the congruence or similarity between two triangles. SAS stands for Side-Angle-Side.
SAS Congruence Rule
The Side-Angle-Side theorem of congruency states that, if two sides and the angle formed by these two sides are equal to two sides and the included angle of another triangle, then these triangles are said to be congruent.
The SAS Similarity Rule
The SAS similarity criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are similar.
Let us see the applications of SAS triangle formulas in the following section.
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