Parallel Lines and Transversals ProofDate: 09/28/98 at 01:01:19 From: Eric Chan Subject: Geometric Proofs I am a freshman at Monta Vista High School in Cupertino, and I am struggling with Geometric proofs, especially ones that concern transversals. I find memorizing all the theorems and postulates difficult, and it is even harder for me to put them to use, for I am not sure where to put them in. I need help on proving a theorem: "If two angles are cut by a transversal and the same-side angles are supplementary, then the lines are parallel." Thanks, Eric Date: 10/18/98 at 16:47:52 From: Doctor Jaime Subject: Re: Geometric Proofs Hello Eric, If you memorize but you don't understand, it will not be of any use to you, and you will forget rapidly. You must try to understand what you are doing. Let's go to the theorem you give. First draw a diagram this: Let's suppose angles A and B are supplementary. What can you do with this information? You may try to get relations between other elements in the figure, namely angles C and D. It is easy to conclude (do you know why?) that angles A and D are also supplementary. This means that angles B and D must be equal. The same reasoning proves that A and C are equal. You certainly know one theorem that relates equal angles and parallel lines, don't you? You can now conclude. In order to give you a better idea how geometric proofs work and how you solve problems in Geometry please read some answers in the High School/Geometry section of Dr. Math: http://mathforum.org/dr.math/tocs/geometry.high.html There is a lot of helpful stuff in there. If you need more help don't hesitate to write us back. - Doctor Jaime, The Math Forum http://mathforum.org/dr.math/ |
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