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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 27 Page 579

Apply the Corresponding Angles Theorem, then write a proportion using the Corollary to the Triangle Proportionality Theorem.

x=48 and y=72

Practice makes perfect

Let's analyze the given figure.

Notice that since the segments formed on the right part of the diagram are congruent, we can solve the equation 13y-6 = 66- 23y to find y.

1/3y-6 = 66-2/3y

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Solve for y

LHS+6=RHS+6

1/3y = 72-2/3y

LHS+2/3y=RHS+2/3y

y=72

Since the three marked right angles are congruent, according to the Corresponding Angles Theorem all three horizontal lines are parallel to each other.

Since we are given three parallel lines that intersect two transversals, we can use the Corollary to the Triangle Proportionality Theorem.

The lengths of the segments intercepted on the transversals are proportional. Let's write a proportion using the expressions for the lengths of the segments. 14x+5/12x-7 = 13y-6/66- 23y Since we know that two segments on the right part of the diagram are congruent, we know that two segments on the left side are also congruent. Let's solve the equation 14x+5 = 12x-7 to find x.

1/4x+5 = 1/2x-7

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Solve for x

LHS+7=RHS+7

1/4x+12 = 1/2x

LHS * 4=RHS* 4

x+48=2x

LHS-x=RHS-x

48=x

Rearrange equation

x=48

We found that x=48 and y=72.

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Exercises p.577-581