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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 1 Page 577

Write a proportion using the Triangle Proportionality Theorem.

10

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. XN/NZ=XM/MY ⇕ 6/9=4/MY Let's solve it for MY.

6/9=4/MY

▼

Solve for MY

LHS * MY=RHS* MY

6/9MY=4

LHS * 9=RHS* 9

6MY=36

.LHS /6.=.RHS /6.

MY=6

We found that MY=6. We can also see that XY=XM+MY. Let's find XY.

XY=XM+MY

XM= 4, MY= 6

XY= 4+ 6

Add terms

XY=10

Subchapter links

Exercises p.577-581