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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 7 Page 577

Recall the Triangle Proportionality Theorem.

2360.3 ft

Practice makes perfect

We are given a part of a city map. We want to find the distance between 5th Avenue and City Mall along Union Street. Let x be that distance. Now, let's consider the given map. We will label the vertices with consecutive letters.

Let's begin by recalling the Triangle Proportionality Theorem.

Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths.

Since we are given that CD is parallel to BE, we can write a proportion. AB/BC=AE/ED We can find the length of AE by subtracting the length of ED from the length of AD. Let's do it! AE = 3201 - 1056 ⇔ AE = 2145 Now, we can substitute the lengths of the segments into the proportion and solve for x.

AB/BC=AE/ED

SubstituteValues

Substitute values

x/1162=2145/1056

▼

Solve for x

Cross multiply

x* 1056= 2145* 1162

Multiply

1056x=2 492 490

.LHS /1056.=.RHS /1056.

x=2360.3125

Round to 1 decimal place(s)

x≈2360.3

The distance between 5th Avenue and City Mall along Union Street is approximately 2360.3 feet.

Subchapter links

Exercises p.577-581