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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Parts of Similar Triangles

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Exercise 20 Page 588

Write a proportion using the Triangle Angle Bisector Theorem.

7

Practice makes perfect

Let's analyze the given figure.

Since we are given a triangle with a segment that is bisecting one of the angles, we can use the Triangle Angle Bisector Theorem.

This theorem tells us that an angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides. We are given the expressions for the lengths of these sides and segments, so we can write a proportion. 18/2x+1 = 24/3x-1 Let's solve it using the Cross Product Property.

18/2x+1 = 24/3x-1

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Solve for x

Cross multiply

18(3x-1)=(2x+1)24

.LHS /6.=.RHS /6.

3(3x-1)=(2x+1)4

Distribute 3

9x-3=(2x+1)4

Distribute 4

9x-3=8x+4

LHS+3=RHS+3

9x=8x+7

LHS-8x=RHS-8x

x=7

We found that x=7.

Subchapter links

Exercises p.586-590