body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

Continue to next subchapter

Exercise 11 Page 577

Write a proportion using the Triangle Proportionality Theorem.

15

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

AB= 12, AC= 16

12+BC= 16

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

▼

Solve for AE

Calculate quotient

3=AE/5

LHS * 5=RHS* 5

15=AE

Rearrange equation

AE=15

Subchapter links

Exercises p.577-581