HELP in indirect proofs??for geometry...?

Question

i dont get the point of indirect proofs...i dont get how to do them..its confusing me...help me understand it...plz...

for any question...dont get the point across my head!

Answer 1

In a direct proof, you take the information that you have been given, draw some of the logical consequences of this information, if necessary draw more conclusions from these consequences, and continue until you arrive at the statement you want to prove.

In an indirect proof, you first assume that the opposite of what you are trying to prove is true and include this in the information you have been given. Then you draw logical conclusions from this information until you arrive at a contradiction or a statement that is obviously false. Since a contradiction or false statement cannot be the consequence of true statements, you have to conclude that the assumption you made in the beginning (that the opposite of what you are trying to prove is true) is a wrong assumption. Therefore the opposite of what you are trying to prove is false, and so the statement you are trying to prove must be true.

Here is a really simple indirect proof in geometry:
Show that no triangle has two obtuse angles.

First assume the opposite statement, that there is a triangle ABC such that angle A and angle B are both obtuse. Since the measure of an obtuse angle is > 90 and since the measure of angle C >0, then the sum of the angles of triangle ABC = Measure of angle A + measure of angle B + measure of angle C > 90 + 90. But we know that the sum of the angles of any triangle always equals 180, so we have a contradiction. Therefore the assumption is wrong, and so no such triangle ABC exists. Thus we have indirectly proven that no triangle has two obtuse angles.

Answer 2

An indirect proof is started by stating the opposite of what you are trying to prove. In this case you would state OM is congruent to NP then go about showing that this could not be true. I could do more with a picture. I hope this helps though.

Answer 3

Hmm...

I skipped geometry. However, I did take trigonometry and pre-calculus, and they had proofs. I was told these proofs were much easier than the geometry ones. But I'd love to try to help also. Maybe put a question in the details.

Answer 4

I wish I could. Add a question and everything you know under details and I can try. I took geometry in high school and all I can rememebr is they were very long and tedious.

TT
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