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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 3 Page 577

By the Converse Triangle Proportionality Theorem, if a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, then the line is parallel to the third side of the triangle.

Are the Segments Parallel? Yes.
Explanation: AD/DC = BE/EC = 2/3

Practice makes perfect

We are given a triangle △ABC and we want to determine whether the segments DE and AB are parallel.

By the Converse Triangle Proportionality Theorem, if a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, then the line is parallel to the third side of the triangle. Let's check if the sides are divided proportionally. AD/DC ? = BE/EC Since we are given lengths of BE and BC, we can find length of EC.

BE+EC=BC

BE= 6, BC= 15

6+EC= 15

LHS-6=RHS-6

EC=9

Now we can substitute all known lengths to our proportion. AD/DC ? = BE/EC ⇕ 8/12 ? = 6/9 We will simplify each ratio as much as possible to see if they are equivalent.

8/12 ? = 6/9

a/b=.a /4./.b /4.

2/3 ? = 6/9

a/b=.a /3./.b /3.

2/3 = 2/3 ✓

As we can see, the sides are divided proportionally. Therefore, segments DE and AB are parallel.

Subchapter links

Exercises p.577-581