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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Scale Drawings and Models

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Exercise 31 Page 605

Write a proportion using the Triangle Angle Bisector Theorem.

12

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 the two segments opposite the bisected angle are proportional to the two other sides of the triangle. We are given the expressions for the lengths of these sides and segments, so we can write a proportion. 8/18-8 = x/15 Let's solve.

8/18-8 = x/15

▼

Solve for x

Subtract term

8/10 = x/15

.LHS /2.=.RHS /2.

4/5 = x/15

LHS * 5=RHS* 5

4/5 * 5 = x/15* 5

FracMultDenomToNumber

a/5* 5 = a

4 = x/15* 5

MoveRightFacToNum

a/c* b = a* b/c

4 = x * 5/15

SplitIntoFactors

Split into factors

4 = x * 5/3 * 5

Cross out common factors

4 = x * 5/3 * 5

CancelCommonFac

Cancel out common factors

4 = x/3

LHS * 3=RHS* 3

4 * 3= x/3 * 3

FracMultDenomToNumber

a/3* 3 = a

4 * 3= x

Multiply

12 = x

Rearrange equation

x = 12

Subchapter links

Exercises p.602-605