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  • one year ago

I'm SOO bad at proofs and I always get confused with them. Could someone help me please???? http://static.k12.com/eli/bb/811/7537/0/2_36627_44211/7537/82f838899777dd887ab22867743c16071a3c95d3/media/fa30df407d1ed47040fb68b1315de7aa0b496523/mediaasset_649531_1.gif Complete a 2 column proof. Given: angle JKN is congruent to angle LMN. Given: angle LKN is congruent to angle JMN.

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  1. Owlcoffee
    • one year ago
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    So, as a little foreword to you, as a tip when writing formal proofs and deducing data, since it's the main goal in Euclidean geometry. Whever we write a proof, we will always... ALWAYS, work with the given information an pre-knowledge of geometry. With that I mean, you only have to relate the given information to draw a conclusion and with the new data, you can go further. To the given information we call "hypothesis" wich, in difference of the verbal definition of "hypothesis", as a mathematical definition it means information that is true. So, going back to Decart who, I quote, said: "To conclude something true, the premises wich it derived from, must also be true". So for that reason, the best way to start off with a proof is to associate the hypothesis, meaning, the informaton we were given. Let's do that: Hypothesis: (1) <JKN = < LMN and (2) <LKN=<JMN Now, from the hypothesis (1) I can draw one conclusion: segment JK is parallel to the segment LM. why?, because of the property of a line intersecting two parallel lines, that is called "altern internal angles". And since those two angles, have in common the segment KM, then all the conditions for the property is satisfied and we can say with no hesitation that indeed, those two segments are parallel. We'll call it (3) JK // LM ("//" means "parallel"). We can do exactly the same with the hypothesis (2), and draw the same conclusion for the exact same reason, altern internal angles, which we'll call "(4)": (4) JM//KL. This is all we need to conclude that we are indeed in front of a parallelogram. Since the parallelogram is a cuadrilateral with two pairs of parallel sides, we can conclude, that the figure JKML is a parallelogram, why?, because of the very definition of cuadrilateral and parallelogram, let's call it (5): (5) JKLM is a parallelogram. As you can see, having a very solid base and understanding of previous definitions of geometric bodies and the base properties of the euclidean geometry is a requirement for solving excercises like these. I'll leave the duty of writing it as a two-column proof to you.

  2. anonymous
    • one year ago
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    Thank you so much for taking the time to type the whole answer AND explain. It makes a lot more sense to me now. Thank you! @Owlcoffee

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