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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 15 Page 582

To find the value of x, note that two segments are congruent.

x=3, y=8

Let's analyze the given figure.

Note that two segments are marked as congruent. Therefore, they have the same length. 8x-18=12-2xLet's solve the above equation for x.

8x-18=12-2x

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Solve for x

LHS+2x=RHS+2x

10x-18=12

LHS+18=RHS+18

10x=30

.LHS /10.=.RHS /10.

x=3

Now that we know that x= 3, we can find the lengths of two segments of the diagram.

Length	Substitute	Simplify
8x-18	8( 3)-18	6
12-2x	12-2( 3)	6

Let's visualize this new information in the diagram.

Let's now find the value of y. Since two marked angles are congruent, according to the Corresponding Angles Theorem, the segment in the middle of this triangle is parallel to one of its sides.

Therefore, we can use the Triangle Proportionality Theorem. The lengths of the segments intercepted by the parallel lines are proportional. Let's write a proportion using the expressions for the lengths of the segments. 5y+16/7y = 6/6 Finally, we will solve the above equation for y.

5y+16/7y = 6/6

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Solve for y

a/a=1

5y+16/7y = 1

LHS * 7y=RHS* 7y

5y+16 = 7y

LHS-5y=RHS-5y

16 = 2y

.LHS /2.=.RHS /2.

8=y

Rearrange equation

y=8

We found that x=3 and y=8.

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