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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 2 Page 577

Write a proportion using the Triangle Proportionality Theorem.

24

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 Since we are given the lengths of XM and XY, we can find the length of MY.

XM+MY=XY

XM= 2, XY= 10

2+MY= 10

LHS-2=RHS-2

MY=8

Now we can substitute all known lengths into our proportion. XN/NZ=XM/MY ⇕ 6/NZ=2/8 Finally, we will solve this equation for NZ.

6/NZ=2/8

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Solve for NZ

LHS * NZ=RHS* NZ

6=2/8NZ

LHS * 8=RHS* 8

48=2NZ

.LHS /2.=.RHS /2.

24=NZ

Rearrange equation

NZ=24

Subchapter links

Exercises p.577-581