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# Geometry MM: Triangles 3 (Merchant, Mizzenmast Mercantile): NWN 0098

After speaking with the priest of Helm she intends talking to one of the militia soldiers standing guard outside the nearby house, but then notices a store to her left called the Mizzenmast Mercantile is open. Never one for missing an opportunity to go shopping, Zanzi decides to forgo talking to the soldiers for the moment and enters the store instead. Inside she asks the burly-looking merchant to show her his wares. Unlike the priest of Helm, this fellow's reaction to Zanzi is favourable, so she knows he will charge her less for goods she'd like to buy and pay her more for items she'd like to sell. Transactions duly ensue during which Zanzi sells a few gems and purchases maps for all the four districts surrounding Neverwinter City Core.
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As before, Zanzi turns on her wire-frame vision to see the polygon constructs that will enable her to estimate how honest this merchant is during transactions, but in this instance she finds that this NPC has countermeasures installed which prevent her from directly analysing his polygons by artificially scaling up or down polygons which are in fact corresponding. She is only able to estimate congruence using what appear to be similar looking triangles that have a side, a side and an angle of the same measure (SSA) and triangles that have all their corresponding angles the same measure (AAA), but these measurements are not sufficient to determine how honest the merchant is during transactions. Therefore she tries another approach based on proofs derived from the fact that corresponding parts of congruent triangles are congruent (CPCTC). Firstly she uses a proofs method (either two-column proofs or flowchart proofs) to compare various similar-looking triangles in the polygon constructs of the merchant's eyes to prove they could be corresponding and then, using her own subterfuge software, scales back down or up to a 1:1 ratio those similar-looking triangles to prove they are congruent. The upshot of all this trickery is that she is able to confirm the merchant's honesty in his transactions despite his attempts to block her analysis, it just takes her a few thousandths of a second longer to do so.
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As an aside, Zanzi discovers a vulnerability in the merchant's countermeasures, namely that his software does not block her analysing isosceles triangles within his polygon constructs. Zanzi is able to exploit this to measure the congruent sides and base angles of these triangles, digitally construct an angle bisector and use comparative data she holds on known altitude and median values for this class of NPC to show no distortion of these polygons is taking place while she and the merchant are engaged in buying and selling transactions. However this procedure takes Zanzi a lot longer to complete owing to the scarcity of isosceles triangles in the constructs within this NPC.