How to construct a geometric proof?

I'm in ninth grade geometry and my teacher is sick, we have a sub but she isn't very good at explaining things. Can somebody explain to me how to construct a proof? All help is appreciated.

Relevance
• xyzzy
Lv 7
4 years ago

All statements must logically follow from what came before.

In 9th grade geometry, all statements must have a reason.

You are allowed to assume that a line that is drawn in a figure is straight. The figure is generally accurate, but is not precise. Other than that, assume very little else.

1st step, before you write anything, look at the problem. Best to decide that what you are proving is in fact true before you start formally writing the proof.

Can you see it? If you can, can you explain how you know this?

If you can't, write down the definitions of all key words, and then write down things you might know that are associated with these key words.

Draw the figure.

Mark up any angles that you know are equal to one another, any sides that you know are equal, any lines that you know are parallel.

Can you see it now?

write down what you have been given. Propose some new information, provide a reason. Ideally your reasons are either, givens definitions, axioms (postulates) or theorems.

here is a really simple example:

Given: AB and CD intersect at E

See figure

Prove angle AEC = angle DEB

you look at it, and you say AEC has some measure.

angles AEC + CEB = 180 degrees

and BED + CEB = 180 degrees

AEC = 180 - CEB = CED

Now, you should try to be a little bit more formal in your proof.

proposition | reason

AB is a line | given

CD is a line | given

E is on AB| Given

E is on CD| Given

AEB is a straight angle | A point on a line forms a straight angle

CED is a straight angle |

AEB has 180 degrees | definition of straight angle

CED has 180 degrees |

AEC is supplementary to CEB | Angles that sum to 180 degrees are supplementary.

BED is supplementary to CEB

AEC = CEB | angles supplementary to the same angle are congruent.

QED (which is Latin for it is proven. It is customary to let the reader know that you have reached your conclusion. A little square at the end is the more modern convention.)

When you have done a few dozen, you can be a little bit less formal.