GED Math: Transversals

Yeah, I know. Trans-what? GED math test don’t expect you to recognize lots of vocabulary like “transversal,” but you gotta know the ideas, right? It all about ideas. Here we got one of the GED geometry ideas. Geometry… that’s shapes, lines, and angles. Not too hard, cuz you can visualize it, y’know? And, I’m gonna show you somethin’ pretty cool… let’s take a look at what’s called a transversal.

Okay, here’s some real GED math. You got all these lines, man, whatd’they mean? Sort of just floating out there, with nothing to attach them to. Where’s the reality? Well, you gotta know that lines and angles are all around. Roads cross at angles, artists use angles to draw, fence posts and construction frameworks, bridge frameworks, all use real-life lines and angles.

But for now, let’s look at the abstraction… the idea. Lines AG and BH are parallel. See, you call a line by the two points it passes through. Line AG passes through point A and point G. Sometimes it’s given as AG with a line above it. You can see that line AG and BH look parallel, because they look like they’re goin’ in the same direction, right? Well, they are parallel.

Now, angles are given by three letters. For example, Angle BDC is 33 degrees. Sometimes, it’ll have a little sideways V to indicate “angle.” Now, when you got two parallel lines, crossed by another line, the line that crosses the other line is the “transversal.” Basically, that means it goes across. And, you can see the transversal crossing parallel lines makes 8 angles. You got 4 angles around point D, and 4 angles around point E.

Here’s what’s cool. The diagram gives only 1 angle. Angle BDC is 33 degrees. From that, I can tell you the measure of ALL the angles. Just by thinking it through, logically. Here’s a hint: two angles that make up a straight line (like BDC and CDH) add up to 180 degrees. Why? It’s half a circle, and a circle is 360 degrees.

Okay, with this info, can you fill out all the angles? Start with the ones around point D.

Angle BDC = 33 degrees

Angle CDH = ???

Angle HDE = ???

Angle EDB = ???

Go on, give it a try.

How’d'ya do? Well, you got Angle BDC, and Angle BDC + Angle CDH = 180, right? So:

33 + CDH = 180

CDH = 180 – 33 = 147 degrees

Now you got 2 angles. Well, CDH +  HDE gotta equal 180, too, right? So, since CDH is 147, HDE is 33 degrees, same as BDC. That leads you to this fact: When two straight lines cross, the opposite angles, across from each other, are always the same. Cuz, the angles next to each other gotta equal 180, you gotta come to the conclusion that opposite angles are the same measurement. Always! So, you don’t even gotta do math to figure out Angle EDB. It’s opposite from CDH. So it the same. It’s 147.

Angle BDC = 33 degrees

Angle CDH = 147 degrees

Angle HDE = 33 degrees

Angle EDB = 147 degrees

That’s 4 angles out of the way. Now, here’s some more facts:

1. Two parallel lines are positioned at the same angle as each other.
2. A straight line is positioned at the same angle as itself (no kidding). What I’m getting at, is any two segments (or parts) of the same straight line go at the same angle as each other.
3. Therefore… what can you say about the angles formed by a Line A crossing Line B and the angles formed by Line A crossing a line parallel to Line B? Think about it… and look at the diagram.

Do you get it? The lines crossing Point D and the lines crossing Point E make the same pattern. Because the two lines that the transversal goes across are parallel, the sets of angles are THE SAME. So, no guessing needed, no math needed, the other angles have the same measurements:

Angle AED = 33 degrees

Angle DEG = 147 degrees

Angle GEF = 33 degrees

Angle FEA = 147 degrees

That’s all the angles. You can figure them all out from one angle. So, once you got one, you got them all. And that makes for some easy GED questions! Good studyin’!

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.