![]() The second option, SSA, does not uniquely identify a triangle, except when the angle is equal to 90°. The theorems like the law of cosines, sines, and others are followed to determine the third side so that we can call SAS as Side-Angle-Side triangle for possible combinations. Thus, you can identify the triangle by the side length and the two angles on either side. The SAS triangle calculator helps perform the mathematical operations on the two sides with specified angles. Why? Because if you know two angles of a triangle, you automatically know the third angle since all three must add up to 180. The first option, AAS, is actually equivalent to ASA. An included angle is an angle formed by two given sides. ![]() The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. The 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. Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. You can simply construct a Side-Angle-Side triangle using a compass. Video Examples: SAS Triangle Congruence Postulate Explained. Why Not AAS or SSA?You may wonder why there are no options for AAS (two adjacent angles and a side length not between the angles) or SSA (two adjacent sides and an angle not between the sides). The SAS Criterion stands for the Side-Angle-Side triangle congruence theorem. Constructing SAS triangles entails two known triangle sides and one angle measurement. The angle between any two sides of a triangle is called the included angle of the triangle. Example 1 In this triangle we know: angle A 49 b 5 and c 7 To solve the triangle we need to find side a and angles B and C. ![]() You can find the equations for triangular area in the related article, " How to Compute the Area of a Triangle: SSS, SAS, ASA, Base Height." The formulas for computing missing angles and side lengths can be found in the Trig and Angles Formula Sheet. The SAS triangle calculator helps perform the mathematical operations on the two sides with specified angles. To solve an SAS triangle use The Law of Cosines to calculate the unknown side, then use The Law of Sines to find the smaller of the other two angles, and then use the three angles add to 180 to find the last angle. How the Calculator WorksThe calculator uses standard geometry and trig formulas. The calculator below computes the area and unknown angles and sides of a triangle if you input (i) two sides and the angle between-SAS, (ii) two angles and the side between-ASA, or (iii) all three side lengths-SSS. It follows that if you know the SAS, ASA, or SSS values for a triangle, you can compute the missing sides and angles, as well as the area! Triangular laws of congruence state that two triangles are equivalent if they have the same values for side-angle-side (SAS), angle-side-angle (ASA), or side-side-side. ![]()
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