Geometry Strategy – Moving the Sides of a Figure Around

Today I would like to teach you a more advanced geometry strategy that can sometimes be used on standardized tests such as the ACT, SAT, and GRE.

A seemingly difficult geometry problem can sometimes be made much easier by moving the sides of the figure around.

This procedure is best understood with an example:

Example: What is the perimeter, in meters, of the figure below?

Try to solve the problem yourself before checking the solution below.

Solution: Recall that to compute the perimeter of the figure we need to add up the lengths of all 8 line segments in the figure. We “move” the two smaller horizontal segments up and the two smaller vertical segments to the right as shown below.

Note that the “bold” length is equal to the “dashed” length. Thus, the perimeter is

(2)(7) + (2)(5) = 14 + 10 = 24.

Warning: Although lengths remain unchanged by moving line segments around, areas will be changed. This method should not be used in problems involving areas.

Here is one more problem for you to try. See if you can find the best way to move the sides of the figure around to make the problem easy to solve. I will provide a solution to this problem tomorrow.

Example: In the figure below, AB = 2, BC = 8, and AD = 10. What is the length of line segment CD ?

More Problems with Explanations

If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.

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