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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 8 Page 577

Write a proportion using the Triangle Proportionality Theorem.

x=5 and y=8

Practice makes perfect

Let's analyze the given figure. We will start by finding y.

We can see that two segments on the left are congruent, so 3y = 12y+20. Let's solve this equation to find y.

3y=1/2y+20

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Solve for y

LHS * 2=RHS* 2

6y=y+40

LHS-y=RHS-y

5y=40

.LHS /5.=.RHS /5.

y=8

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

If a segment parallel to one of the sides of a triangle is drawn between the other sides, the segment divides the other two sides proportionally.

Let's write a proportion using the expressions for the lengths of the segments. 3y/12y+20 = 20-3x/2x-5 Since we know that two segments on the left side are congruent, we know that two segments on the right side are also congruent. Let's solve the equation 20-3x = 2x-5 to find x.

20-3x = 2x-5

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Solve for x

LHS+5=RHS+5

25-3x=2x

LHS+3x=RHS+3x

25=5x

.LHS /5.=.RHS /5.

5=x

Rearrange equation

x=5

We found that x=5 and y=8.

Subchapter links

Exercises p.577-581