Wednesday, August 8, 2012

To illustrate the concept of similar triangles and the use of proportions, I found a great example from a sample GED test online.

To measure the distance (DC) across a pond, a surveyor takes points A and B so that AB is parallel to DC. If AB = 60 feet, EB = 48 feel, and ED = 80 feet, find DC. 72 ft., 84 ft. ,96 ft., 100 ft., Not enough information is given.

The important thing is that since AB and DC are parallel angles ABE and BDC are congruent (alternate interior angles) as are angles ACD and BAC congruent by the same reason. You will quickly notice that triangles ABE and DEC are similar triangles.  Because of this similarity, corresponding sides are in proportion. DE matches up with  BE, and DC matches up with AB... Create proportions with these sides and set them equal to each other.


80/48 = x/60

To solve this we can multiply the equation by 60

(80/48)(60) = (x/60)60

We multiply by 60 to get x by itself

4800/48 = x

100 = x

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