<p>I read a solution from the consolidated math answers but i didn't really get it. I know it'll be hard to explain because i'll have to be able to visualize and draw it.. but draw the best you can.</p>

<p>Number 15 of page 684. THe cube shown above has edges of length 2 and A B are midpionts of two of the edges. What is the length of AB (not shown)?</p>

<p>What is the likelyhood that a problem like this will show up? I really didn't know how to start..</p>

<p>In order to find the distance from AB, you have to find the line segments I labeled a and b. a and b will then form two legs and you can do the Pythagorean theorem to solve for c (AB). </p>

<p>a in my diagram is itself the hypotenuse of two legs. Do 1^2 + 2^2 = a^2 and solve for a.
Use that value for a and the value for b (1) in another Pythagorean theorem to solve for AB.</p>

<p>i know the smaller triangle created on the side to find a is a right triangle thus the pythagorean thereom can be used. How do you know the bigger triangle is a right angle though?</p>

<p>A cube is made up of squares (obviously), so you know that each of the vertical lines forms right angles with the two lines it meets up with at the base. One of the theorems of geometry is that if a line is perpendicular to two lines in the same plane, it is perpendicular to that plane. So the vertical lines are perpendicular to any line on the plane -> right triangle.</p>

<p>All angles of a cube are right angles. For a simple square, this is very easy to vision. For a cube, you are adding another axis, the z axis (Just thing of a corner of a room. You have three lines meting at one point (these represent the x,y, and z axis's)). In a cube, every angle formed by the intersection of the X axis with the Y axis or the X axis with the Z axis or the Y axis with the Z axis is a right angle.</p>