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Two-column Proof

Date: 5/24/96 at 10:58:52
From: Anonymous
Subject: Proofs

I am a 9th grader and I need help on proofs. My book says: "The proof 
that tangent segments from a point outside a circle to a circle have 
equal lengths was outlined in this lesson. Do a two-column proof on 
this theorem." 

My mom and I can't figure out how to write these proofs. Thanks!

Date: 6/28/96 at 15:36:11
From: Doctor Leigh
Subject: Re: Proofs

Thanx for writing us with your problem.  

A two-column proof is one where you put statements in one column, and 
the reasoning for those statements in another.  For example:

Statements                  |    Reasons

1. point a                  |  1. given (this means that this
   (outside of circle B)    |     information is given in the problem

2. line ac, tangent to B    |  2. given

3. line ad, tangent to B    |  3. given

Once you have defined the givens you are ready to start your proof.  
A good way to do this is to draw yourself a picture, and as you see 
things in the picture write them down in the proof.)

4. choose the midpoint      |  4. Defining a point (this is the
   on the circle between    |     reason why you can do this)
   d and c, name it e       |

5.  Connect ea              |  5. Constructing a line

The proof goes on from here, but I'm going to let you try.  Here's a 
hint: it has something to do with congruent triangles.  Read your 
textbook about theorems dealing with circles and triangles.

Good Luck!

-Doctor Leigh Ann,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
Associated Topics:
High School Conic Sections/Circles
High School Euclidean/Plane Geometry
High School Geometry

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