Two-column ProofDate: 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/ |
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