Geometry: Proof

Question

A proof should always begin with stating the given information.

True or False? Explain

Answer 1

SHort Answer:

As written, my vote is TRUE:

A proof SHOULD always begin with stating the given...

Long Answer:

However, starting with the given is not an absolute requirement. Depending on

the nature of the problem, it is possible to start a proof with something

else other than the given. For example, a reflexive property statement

or quoting a postulate or axiom. Doing so does not destroy the validity

and correctness of the proof.

What that being said, you have to be careful how to start it out.

You cannot quote, for example, the pythagorean rule until you know

you have a right triangle. So if the right triangle is not given, you must

prove it is a right triangle.

Here is an example of what I am talking about.

Given : LIne segment contains points A,B,C,D; A and D are endpoints;

AC = BD

Prove: AB = CD

statement reason

1) BC = BC reflexive

2) AC = BD given

3) AC = AB+BC; given; distance axioms

BD = BC+CD

4) AB + BC = BC + CD : substitution

5) BC + AB = BC + CD : commutative

6) AB = CD : subtraction property of equality

Notice it starts with the reflexive property rather than given;

Also in statement 3; the given is used in combination with

the distance axiom, so not all of the given is used at once.

Answer 2

A proof reasons from what it known. If what is known is not known then one cannot knowing provide a proof.