Math Question

[shams]

kn said:
The SSA theorem (side side angle) does not ALWAYS prove congruency. The inclusion of Trigonometry may or may not prove this particular pair of triangles to be congruent. The fact that the long horizontal line is made up of two congruent (equal length) means bisection proof rules apply. The opposing angles of bisection are congruent and therefore you have the ingredients for an SSA proof BUT SSA is not a definitive theorem to prove congruency. As IOI said, the choice of lines that have been given as congruent along with the intentionally missing right angle or congruency markers for the included angle are provided here to create an SSA ambiguity.

Ok - after further reading, I do believe you are correct.

I found a link to an article earlier today that showed that SSA is sufficient proof - "as long as the angle is opposite the longer of the two equal sides" (?). After looking at this on paper, I can see why SSA is generally not sufficient (what from I can see there are two possible solutions for any triangle given SSA - basically an "inner & "outer" solution).

And I agree with both of you now - the dataset given is intentionally given to expose this ambiguity.

The triangles are NOT congruent!

(interesting question :>)