I have drawn a square holding Shift. It already shows the middle of a line. What I need is that after drawing a line, I can't find the middle spot of the split line. I have shown it in the image I'm attaching.

I think Guides well help:

@blackroz, not sure which middle you're talking about. The lower right quadrant? The easiest way to find the middle is to use the middle-align tool. You can find it under the Arrange pull down menu.

The middle-align tool mentioned above works to get the half-way point of the square (to draw the first horizontal line), but it won't dissect it a second time. Instead, try this:
1) Draw a second horizontal line right over the bottom side of the square
2)Draw a third horizontal line anywhere between the middle line and the bottom line.
3) Select all three horizontal lines and choose "Distribute vertically" from the Arrange tool mentioned above. When three horizontal lines are selected, this will always bring the middle one to the half-way point between the top and bottom lines.

Thanks for the help but this is very exhausting and time consuming since I have to make a lot of them. I'm surprised that there isn't a simpler way to do this.

You could draw a temporary rectangle from one line to another. That shape has handles, which makes it easier to pull a guideline towards the middle of it. (see picture)
Since you have to make a lot of them, you can copy or cut the rectangle from one slide to another.

Attached Images

middleOfLine.JPG (16.2 KB, 16 views)

You could replace your drawing with a table. That way you can distribute rows and columns evenly (or unevenly, for the right upper part), and splitting a cell will cut it exactly in half.

Attached Images

middleOfLine_02.JPG (13.5 KB, 16 views)

See image - making this table took about two minutes.

Attached Images

middleOfLine_03.JPG (8.3 KB, 16 views)

Well if you used ryanbrewer110's option you technically only have to do it once. Afterwards, group the lines to form one object then copy/paste to the next and adjust to the top and bottom of the quadrant you're trying to find. The middle line will always be in the center.