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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 81 Page 659

Use the Triangle Proportionality Theorem or its Corollary.

x=1, y=3/2

Practice makes perfect

Consider the given triangle.

We are asked to find the values of x and y. We will do it one at a time.

Finding x

Note that the segments with lengths 2x+3 and 6-x are congruent. Therefore, their measures are equal. 2x+3=6-x Let's solve the equation using the Properties of Equality.

2x+3=6-x

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Solve for x

LHS+x=RHS+x

3x+3=6

LHS-3=RHS-3

3x=3

.LHS /3.=.RHS /3.

x=1

Finding y

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

Let's write an equation in terms of y using the above theorem. 4/3y+1=2y Now we will solve the equation.

4/3y+1=2y

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Solve for y

LHS * 3=RHS* 3

3(4/3y+1)=6y

Distribute 3

4y+3=6y

LHS-4y=RHS-4y

3=2y

.LHS /2.=.RHS /2.

3/2=y

Rearrange equation

y=3/2

Subchapter links

Exercises p.655-659