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### Two Column Proof of a Theorem

```
Date: 08/12/98 at 15:39:41
From: Brandon Pendrys
Subject: Two Column Proof of a Theorem

I homeschool, and this question really has me stuck.

Q. Write a two-column proof for the following theorem. Give numbered
statements with reasons.

Given: AC > BC and AP = BQ
To Prove: PC > QC

c
^
/    \
p/       \q
/          \
a/_____________\b

I Set my proof up like this so far:

STATEMENT      |      REASON
----------------------------------------------------
1. AC>BC and AP=BQ      |   1. Given
2.                      |   2.

Now how do I know what to do next and how do I figure my reason?

Thank you for your time.
Brandon Pendrys
```

```
Date: 08/12/98 at 16:30:58
From: Doctor Rob
Subject: Re: Two Column Proof of a Theorem

The next step is "AC = AP + PC" and the reason is "The whole is the sum
of its parts." The following step is "BC = BQ + QC" with the same
reason.

Next substitute from steps 2 and 3 into the inequality in step 1, with
the reason "Substitution."  Finally subtract AP = BQ (step 1) from both
sides of the inequality in step 4, reason, "Equals subtracted from
unequals are unequal in the same sense," (or whatever wording your
teacher thinks reflects the correctness of this operation).

Finally, simplify the resulting inequality to get your answer.

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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