Proofs help!?

Question

what would be indirect proofs for these?
Given: m<1 =/(not equal ) m< 2
Prove: Tri.ABC is not an isosceles triangle with vertex B.


2.Given: m<1 + m<2 =/(Not equal) 180
Prove: a is not parrallel to b

Answer 1

1. A triangle is isosceles if and only if it has 2 equal sides. Isosceles triangle theorem says a triangle is isosceles if and only if the angles opposite the equal sides are equal. Taking half of the biconditional, if the triangle is isosceles, m<1 = m<2. Since m<1 not = m<2, by indirect argument (or whatever your book calls it), triangle is not isosceles.

2. Needs diagram. Parallel lines and a transversal? Then if lines parallel, same side interior angles are supplementary, that is, m<1 + m<2 = 180. Since not, not.

Answer 2

Ugh. I am in 8th grade and geometry and I have to say, Indirect Proofs are the worst thing so far this year. It is kind of hard to work w/ w/out a picture, and you really shouldn't use Yahoo! Questions to do homework, but I can try and help a little, to understand it at least. If this helps, the first step for each should be the opposite of what you are trying to proove.

For no. 1: 1. Tri. ABC is an isosceles tri. w/ vertex B
For no. 2: 1. a is parallel to b

From there, you try to proove the opposite of the given. By prooving that the first step contradicts the given, you proove that the first step is false. Thus, you proove the opposite is true, which is originally what you were trying to proove.

Sorry that sounds confusing, but its hard to not do it in person. If you need extra help, you need to ask your teacher. Good luck.

Answer 3

what is m ?