Exercise 11 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 lines 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 AB and AC, we can find the length of BC.

AB+BC=AC

SubstituteII

AB= 12, AC= 16

12+BC= 16

SubEqn

LHS-12=RHS-12

BC=4

Now we can substitute all known lengths into our proportion. AB/BC=AE/ED ⇕ 12/4=AE/5 Finally, we will solve this equation for AE.

12/4=AE/5

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Solve for AE

CalcQuot