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McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 26 Page 579

Write a proportion using the Triangle Proportionality Theorem.

x=10 and y=3

Practice makes perfect

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

We can see that two segments on the right are congruent, so 2y+1 = 5y-8. Let's solve this equation to find y.

2y+1 = 5y-8

▼

Solve for y

AddEqn

LHS+8=RHS+8

2y+9 = 5y

SubEqn

LHS-2y=RHS-2y

9 = 3y

DivEqn

.LHS /3.=.RHS /3.

3=y

RearrangeEqn

Rearrange equation

y=3

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. 15x+3/4x-35 = 2y+1/5y-8 Since we know that two segments on the right side are congruent, we know that two segments on the left side are also congruent. Let's solve the equation 15x+3 = 4x-35 to find x.

1/5x+3 = 4x-35

▼

Solve for x

AddEqn

LHS+35=RHS+35

1/5x+38 = 4x

MultEqn

LHS * 5=RHS* 5

x+190 = 20x

SubEqn

LHS-x=RHS-x

190=19x