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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 9 Page 611

First, use Corresponding Angles Theorem. Then, recall Congruent Parts of Parallel Lines Corollary.

x=0.5, y ≈ 1.67

Let's analyze the given figure.

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

Since these three vertical lines are parallel and they cut bottom transversal forming two congruent segments, we can use the Congruent Parts of Parallel Lines Corollary.

The lengths of the segments intercepted on the upper transversal are also congruent. Let's use this information and expressions for the lengths of the segments to write equations to find x and y. Knowing that XY=YZ we can write an equation 5x+8 = 21x to find x.

5x+8=21x

▼

Solve for x

LHS-5x=RHS-5x

8=16x

.LHS /16.=.RHS /16.

8/16=x

a/b=.a /8./.b /8.

1/2=x

Rearrange equation

x=1/2

Calculate quotient

x=0.5

Since AB=BC, we can solve an equation 20y-2 = 17y+3 to find y.

20y-2=17y+3

▼

Solve for y

LHS+2=RHS+2

20y=17y+5

LHS-17y=RHS-17y

3y=5

.LHS /3.=.RHS /3.

y=5/3

Calculate quotient

y=1.666666 ...

Round to 2 decimal place(s)

y ≈ 1.67

We found that x=0.5 and y ≈ 1.67.

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