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Parallel Lines and Transversals Proof


Date: 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/   
    
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
Middle School Geometry
Middle School Two-Dimensional Geometry

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