A two column proof is a method to prove statements using properties that justify each step. The properties are called reasons. All reasons used have been showed in previously algebra courses. We will in the following video lesson show how to prove that x=-y2 using the two column proof method.

The ruler postulate tells us that two points on a line can be paired with real numbers so that, given any two points A and B, A is zero and B is a positive real number.

Further on the segment addition postulate tells us that if a point B is somewhere between point A and point C then AB + BC = AC.

Similar relationship is the angle addition postulate. If we have the following angles:

then mBAD + mDAC = mBAC

Video lesson: Solve the following algebraic equation using logic

2 (x + ½) = 0

To see the solution look at the video in the next page.

Here we have an algebraic equation and we’re going to very carefully go through each step and explain those steps so that we can solve for x. So let’s start at beginning, this is a given, this is what we’re trying to solve, this equation. So what we want to get to of course is x equals something. So let’s do each step and discuss each step along the way. So here we have 2 (x + ½) = 0 is our given. Then we want to distribute, it’s a distributive property. We’re going to basically simplify this as much as possible until the very end. So the distributive property says we multiply through by 2. So multiplying this quantity by 2 give us 2 times x and 2 times one half, that’s a distributive property. Now when you do any algebraic equation that you’re solving for x at each point after you do something you need to simplify. So we’ve done the distributive property, then we need to simplify it. So 2x stays the same, two times one half is just 1. So we have to simplify after each step that we do something. The next step that we’re going to do something is an inverse operation of addition. We need to get rid of this +1 and the inverse operation of addition is subtraction so we’re going to use the subtraction property. If we subtract 1 from here we have to subtract 1 from the other side. So when we do that and we simplify and 1 -1 is 0 so we’re just left with 2x, 0 – 1 is -1. So we need to do the next step we have an x here, 2 times x. The inverse operation of multiplication is division so we’re going to use the division property. 2x divided by 2 and then we have to divide by 2 on the other side, -1 divided by 2. Then we simplify, 2x divided by 2 is just x and this stays the same. So x equals negative one half after we simplify it. That’s our final answer; we have x on one side and everything else on the other so we’re finally done here.