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McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 13 Page 577

Write a proportion using the Triangle Proportionality Theorem.

Practice makes perfect

Let's analyze the given figure. Since we are given a triangle with a line that is parallel to one of its sides, we can use the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. AB/BC=AE/ED Since we are given the lengths of AE and AD, we can find the length of ED.

AE+ED=AD

SubstituteII

AE= 12, AD= 27

12+ED= 27

SubEqn

LHS-12=RHS-12

ED=15

Now we can substitute all known lengths into our proportion. AB/BC=AE/ED ⇕ 8/BC=12/15 Finally, we will solve this equation for BC.

8/BC=12/15

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Solve for BC

MultEqn