Congruent triangles....why not SSA?

Question

If the two sides of two triangles are equal and one angle, which is next to that two sides of two triangles are equal, why we cannot say that they are congruent (SSA)?

Answer 1

You can construct an example of two triangles satisfying SSA that are not congruent.

Answer 2

Because if the angle we know is equal to its counterpart and is smaller than 90 degrees, its opposite side can intersect with the unknown side at one of two points.

Answer 3

Because you can make more than 1 kind of triangle with this criteria. For example, the first triangle has a degree angle between the two known sides, and the second has a (180-a) degree angle between the two known sides. The criteria you show satisfy these two triangle

Answer 4

http://i34.tinypic.com/2qmp4ip.jpg

S(blue) and S'(red) are radii of the circle,

so they are equal in length.

Therefore, S(blue)S(black)A = S'(red)S(black)A

But the two triangles are not congruent.

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