Geometry Strategies - Part I

Lesson by Mike McGarry
Magoosh Expert
Now we can talk about some geometry strategies. Geometry is primarily visual, and it demands visual as much as logical skills. So, always do geometry with a diagram. It's very important to use the visual part of your brain in thinking through geometry. Sometimes the problem will give you one.

If it doesn't, draw one of your own. And even if it does, it's good to redraw it on your scrap paper too, so you can mark it up yourself. So what do I mean by this? So, when you draw it yourself, you can add any information given in the problem. Because sometimes information will be given in the text, but it won't be in the problem that the test gives.

And then, you can also add any information that you can deduce yourself. Remember the little square is a very good abbreviation for perpendicular. The test also uses that symbol. Arrows, such as this, are good symbols for parallel, to show two lines are parallel. Now, the test will not use these symbols, but it's still a very good abbreviation to use in your own diagrams.

It may be helpful to extend lines in a diagram, or to add a line that will facilitate a calculation. And we'll see this as we move through this module. In some problems it'll be helpful to assign variables, either to the lengths or to the angles. So that you can use algebra to solve.

And finally, you need the visual ability to dissect a diagram. Now what do I mean by this? And the best way to explain this is with this practice problem. So here's a practice problem. Pause the video and find x. Okay, let's talk about this.

Now you may look at this and you may think, oh dear, okay. So, let's see, we have to find this angle, and this angle, and that would allow us to find that angle. And then we can slowly work our way over, maybe we can find one of the angles over here, or over here someplace. Well, that's gonna be a laborious way to go about this problem.

And it's not really clear that that's even going to allow us to solve. Well, notice the following. Instead of looking at all these little triangles here, instead, we can look at this one big triangle. And of course in any triangle, the sum of the three angles has to be 180 degrees. It doesn't matter the size of the triangle.

It could be a big triangle or a small triangle. Here's a big triangle. We know the 95 we know the 40, we want the x. So x = 180- 95- 40. So x is 45. So it's very important when you have a diagram with a lot of detail, that your able to go back and forth, look little and look big.

Because, of course, anything that's true of a little triangle could also be true of a big triangle. So, very important skill. In summary, always draw a diagram. Even if one is given it's good practice to draw it yourself. You get your hands involved.

That involves part of your brain. You involve your visual intelligence. Very important. Then you can label it with what you are told and what you can deduce. You may have to extend a line or introduce a new line. We'll talk more about that in upcoming lessons.

You may have to assign variables to lengths or angles and do some algebra. And finally, in diagrams remember to look big and look small. So, look at all the details as well as look at the larger shapes, and remember that the properties can apply to any, larger or smaller.