No, the SSA congruence rule is not a valid criterion that proves if two triangles are congruent to each other. Is SSA a Criterion for Congruence of Triangles?
If two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the triangles are considered congruent. If three sides of a triangle are congruent to three sides of another triangle, the triangles are considered congruent. SSA congruence rule can prove if triangles are congruent in two scenarios: When Can SSA Prove Triangles are Congruent? The size and shape would be different for both triangles and for triangles to be congruent, the triangles need to be of the same length, size, and shape. The SSA congruence rule is not possible since the sides could be located in two different parts of the triangles and not corresponding sides of two triangles. 
However, this congruence or criterion is not valid. SSA congruence rule states that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal. Listed below are a few topics related to the SSA congruence rule, take a look.įAQs on SSA Congruence Rule What is Meant by SSA Congruence Rule? Therefore, it is proved that the SSA congruence rule is not valid. In other words, congruence through SAS is valid.
A pair of sides and the included angle will uniquely determine a triangle. In other words, congruence through SSA is invalid. A pair of sides and a non-included angle will not uniquely determine a triangle. ∆A 1BC and ∆A 2BC with a pair of sides and a non-included angle. Thus, two different triangles have been successfully constructed i.e. Place the tip of the compass on B such that two points can be marked off on CX as shown in the image below. How many locations of A are possible? Configure the compass such that the distance between its tip and the pencil’s tip is 3cm. Step 3: Take a point A on the ray CX such that AB = 3cm. Step 2: Through C, draw a ray CX such that ∠BCX = 30° If during our construction process, we find that we can construct only one (unique) such triangle, then SSA congruence would be valid, but on the other hand, if we find that we can construct more than one such triangle, then SSA congruence would be invalid because then two different triangles can have the same two lengths and a non-included angle. Let’s try to geometrically construct such a triangle. Suppose that there is a triangle two of whose sides have lengths 4cm and 3cm, and a non-included angle is 30°. Let us consider an example to understand this better. Therefore, the SSA congruence rule is not valid. The two triangles do not have the same shape and size. We see that even though two pairs of sides and a pair of angles are (correspondingly) equal, the two triangles are not congruent. In the two triangles ∆ABC and ∆DEF, we have AB = DE, BC = EF, and ∠C = ∠F (non-included angles). 
As we already learned that this congruence rule is not valid and triangles cannot be congruent, let us see the reasons as to why SSA will not work.
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