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### Proofs and Reasons

```
Date: 01/03/99 at 19:31:12
From: Maggy
Subject: Proofs and Reasons

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
/   \
/       \
/           q
p               \
/                   \
a-----------------------b

STATEMENT                REASON

1. AC > BC and AP = BQ   Given
2. AC-AP = PC            Subtraction property of inequality
3. BC-BQ = QC            Subtraction property of inequality
4. PC = QC               Substitution Property

This is what I have for my answer to the question. My question is: are
steps 2 and 3 correct? I don't think they are but I couldn't find or
think of any other way to do it.
```

```
Date: 01/04/99 at 08:31:24
From: Doctor Jerry
Subject: Re: Proofs and Reasons

Hi Maggy,

From the diagram, I think you want me to assume that P lies between A
and C and Q lies between C and B.

I wouldn't want to say statement 2 is wrong. However, to say that
AC - AP = PC is the "subtraction property of inequality" doesn't
compute with me. I think I'd arrange matters this way:

AC > BC             given

AC - AP > BC - BQ, (the same number can be subtracted from both
sides of an inequality)
PC > QC

I don't know what to call this last step. It's a geometric operation,
not a property of inequalities.

- Doctor Jerry, 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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