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How to Solve a CSSTP Proof

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2016-11-30 18:53:05
Geometry Essentials For Dummies
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CSSTP is an acronym that represents a simple but useful truth: In similar triangles, the Corresponding Sides of Similar Triangles are Proportional. CSSTP proofs often involve an odd step at the end where you have to prove that one product of sides equals another product of sides.

You'll see what this means in the following problem:

geometry-CSSTP

Here's the proof diagram.

geometry-csstp-proof-diagram

You can often use a proportion to prove that two products are equal; therefore, if you're asked to prove that a product equals another product

geometry-prove-statement

the proof probably involves a proportion related to similar triangles. So look for similar triangles that contain the four segments in the prove statement. You can then set up a proportion using those four segments and finally cross-multiply to arrive at the desired product.

Here's the formal proof:

geometry-formal

About This Article

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About the book author:

Mark Ryan has more than three decades’ experience as a calculus teacher and tutor. He has a gift for mathematics and a gift for explaining it in plain English. He tutors students in all junior high and high school math courses as well as math test prep, and he’s the founder of The Math Center on Chicago’s North Shore. Ryan is the author of Calculus For Dummies, Calculus Essentials For Dummies, Geometry For Dummies, and several other math books.