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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 thru geometry. Sometimes the problem will give you one, if it doesn’t, draw one of our own. And even if it does, it’s good to redraw it on your scrap paper to, 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, 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 diagrams. It may be helpful to extend lines in the 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 the angles, so that you can use algebra to solve. And finally, you need the, 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. We 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 the angles over here or over here some place.
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.
Doesn’t matter the size of the triangle. 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 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, 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 the 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.
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