As for the "incorrect notation" issue (which I think was aimed at Hoosie): In your real copy, you would be using the proper symbols, but since it is not easy to enter them all here, you could just state at the beginning that you are using "=" for the congruency symbol, to keep people from objecting. Alternatively, since others have been using it, you could just copy the symbols, as I am doing here from what you quoted in post #10: ∠BAC≅∠BDC , ΔXYZ≅ΔBDC
So here is what you are saying, with the right symbols (except for the bars over segment names):
ΔBAC ≅ ΔBDC:
Identical symbols show BA ≅ BD and AC ≅ DC
BC is a common side to both ΔBAC and ΔBDC (reflexive law).
The three sides of ΔBAC (BA, BC, DC) are congruent to the corresponding three sides of ΔBDC (BD, BC, DC)
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
By SSS (side side side), the two triangles are congruent
Very likely you aren't required to show that much detail; you'll have to ask your teacher about that. In writing proofs, we don't say that we can tell two segments are congruent by the markings on them; we just say that we are told they are congruent! But you're at the beginning of the learning process and not writing full proofs yet, so it's good to think through, and write out, all the details.
So try again if you like, not copying quite so much from Hoosie (e.g., your last two lines are synonymous, so one could be dropped). But this is a math help site, and this is verging on trying to make your English perfect. I'd move on.