Check out triangles below

http://i42.tinypic.com/z1hue.png

Both have 2 congruent sides (red = red, blue = blue) and congruent angle, but triangles are not congruent.

Let a = 5√3, b = 5, B = θ = 30°

Using Law of Sines, we get:

sin(A)/a = sin(B)/b

sin(A) = a sin(B)/b

sin(A) = 5√3 sin(30) / 5

sin(A) = 5√3 * 1/2 / 5

sin(A) = √3/2

A₁ = 60°

A₂ = 120°

C₁ = 180° - 30° - 60° = 90°

C₂ = 180° - 30° - 120° = 30°

Again, using Law of Sines:

sin(C)/c = sin(B)/b

c = b sin(C) / sin(B)

c₁ = 5 sin(90) / sin(30) = 10

c₂ = 5 sin(30) / sin(30) = 5

So with SSA we have two possible triangles:

a = 5√3, b = 5, c₁ = 10

A₁ = 60°, B = θ = 30°, C₁ = 90°

and

a = 5√3, b = 5, c₂ = 5

A₂ = 120°, B = θ = 30°, C₂ = 30°

Mαthmφm