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Geometry Strategies - Part I


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 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 this symbol, but it's still a very good abbreviation to use in your own diagram.

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 will 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 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 going to 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 on 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 small triangle.

Here's a big triangle, we know the 95, we know the 40, we want the x. So x equals 180 minus 95 minus 40 so x is 45. So it's very important when you have a diagram with a lot of detail that you're 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 love your visual intelligence, very important. Then you can label it with what you're 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, in order to remember that the properties can apply to any, larger or small.

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