About doing Math Proofs?

Question

If there's a question that gives u a description of a diagram and tell you to prove something, is it ok if i add extra details(like points) to the diagram and give description about those extra details(such as that the line i inserted bisects an angle, etc) in the "given" section? or do i have to write them in the "statement/reason" section and say something like "contruct point A on BE so that it is the midpoint"?

Answer 1

You should never modify the "given" section. Anything that you add, do it in the actual proof itself. The point is to do the proof given only what you're given, nothing more or less.

Answer 2

The traditional way to do this, to which Yason has alluded, is to "construct" the ingredients you need. Here is the procedure, in general:

(1) Make your Statement/ Reason diagram as you normally would, and list all the "given" information, using the number of statements and reasons that you would normally require to do so.

(2) Now, mark the first of the items you need to mark on the figure, that are not listed, but that you want to use for your proof. The statement is "Construct....."

Example: 4. Construct Point P at the interstection of Segment AC and Line VF.

This would go under "Statements".

THe corresponding reason would just be the reason why you are allowed to label your figure that way, or construct what you have just drawn. In this case, it could certainly be

4. Two non-parallel lines intersect in a unique point.

There are also constructions that require more work than the labelling of a figure. You will want to draw in the entire construction when using one of them, step-by-step. To use them in a proof, record each step of the construction with a statement of what you drew or labelled, and the corresponding reason.

(3) Continue with the proof!

Answer 3

You have to do both assuming you are given a triangle to proof that angles in a triangle = 2 right angles (180 degrees)

if you construct the triangle and have named the angles and sides you have to construct a perpendicular line bisecting one side and name them and in your proof you have to mention that line that you have constructed

Answer 4

if you show the additional deducted results on the diagram show them in parenthesis.

Answer 5

it is always better to solve a problem as simple and fast no need foor those add ons dude