12/8/2023 0 Comments Sas geometry proof example![]() ![]() ∆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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