2.+Plane+Geometry+-+Misconceptions

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Conditions for Congruence
> SSA is not a proof for triangle congrunency. The only triangle congruent proofs involving a combination of angles and sides are > > If you still don't get this, please explore using the wonderful interactive tool at @http://nlvm.usu.edu/en/nav/frames_asid_165_g_3_t_3.html This tool allows you to play with different SSA configurations and prove to yourself you can make different, non-congruent triangles given one set of SSA conditions.
 * **Don't be an ASS! (The Donkey 'proof')**
 * **AAS** - angle, angle and //corresponding// side
 * **SAS** - side, //included// angle, side
 * **RHS** - a very special SSA condition - guaranteed to work because we have a right angle.
 * **Why isn't SSA a condition for congruency?** Because this is the so-called **Ambiguous Case**. In many cases there are two possible triangles that match the condition. You will see this case again when doing the Sine Law - it's exactly the same situation : given two sides and an angle that is not between the two sides, two solutions are possible.
 * **AAA** is not a proof of triangle congruency - that's a proof of triangles are similar.

Conditions for Similarity
> Think: rectangles.
 * Corresponding sides of a similar triangles are not equal - their //ratios// are equal. To prove similarity using side properties, we must show matching ratios are equal.
 * Equiangular polygons are not necessarily similar. We can only say equiangular implied similarity for //triangles//.