Geometry

Two-Step Problems

Words of “Wiz-dom”If there is anything you should always keep in mind about all geometry problems it’s that they are going to be two-step (or more) problems. Think back to the lesson about how to do word problems. Remember that you have some given information and a question you have to answer. There is definitely going to be some information that you need but it is not given directly.  You need to calculate the missing information by using the given information. It is called “calculated” or “derived” information. It is this unspecified information that is necessary to answer the question. For example, you might be given the circumference of a circle but you need to calculate or derive the radius to answer the question. You might be given the length of the side of a square but you might need to calculate or derive the diagonal of the square to answer the question.

 Using Diagrams

Words of “Wiz-dom”Diagrams are the key to most geometry problems. Sometimes they are provided. Sometimes you have to draw them based on information in the narrative part of the question. On the SAT (but not the ACT), the diagrams are drawn to scale unless you are told otherwise. If you see, “Note: Figure not drawn to scale,” you know that you can’t use how the diagram looks to estimate you answer. On all the others, answering questions, making estimates of answers, and using the information to check your answer is highly encouraged. What the heck, if the test writer is going to give you a clue, then use it!

When drawing your own diagrams, you should draw them quickly but as close to scale as you can. When you add something to an existing diagram, attempt to draw it to scale. (Be sure you don’t waste time trying to be an architect, but being close to scale helps.)

Finally, when you encounter diagrams that are not drawn to scale, fix them. Redraw them (without try to be an architect) so they make sense. Sometimes this technique is just the hint you need. If this reminds you of Pillar II: Restate Given Information, then good for you because it is.

Words of “Wiz-dom”-The test writer draws odd shapes and wants to see if you can break them down into regular shapes: triangles, quads, and circles. For example:

 

The strategy for these questions is to look at the unusual shape and break it down into normal geometric shapes. In the first example, you are now working with a square and a triangle. In the second example, you are now working with a circle and a square. The second example is a case of “overlapping” figures. The question may be, “What is the area of the un-shaded region?”

On the test, instead of “unshaded” region questions, these are shaded region questions.  When you see one, and you will, keep in mind they are simply subtraction questions.  Calculate the area of the whole figure then subtract the clear area which will leave you the area of the shaded region.

More words of “Wiz-dom” on Using Diagrams

Geometry Homework

SAT Home Page

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