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McGraw Hill Integrated II, 2012 View details

6. Inequalities in Two Triangles

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Exercise 17 Page 459

Consider the Hinge Theorem.

2< x< 6

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For the given triangles, we will find the range of possible values for x.

In order to do that, we will use the Hinge Theorem to compare the side lengths.

Applying the theorem, we can write an inequality for the side lengths. 57^(∘) > 41 ^(∘) ⇒ 12 > 3x-6 Let's solve the inequality for x.

12>3x-6

AddIneq

LHS+6>RHS+6

18 > 3x

DivIneq

.LHS /3.>.RHS /3.

6 > x

RearrangeIneq

Rearrange inequality

x < 6

All x-values less than 6 will work. In addition, 3x-6 must be greater than 0.

3x-6>0

AddIneq

LHS+6>RHS+6

3x>6

DivIneq

.LHS /3.>.RHS /3.

x>2

Therefore, 2^(∘) is the lower limit of x. We can determine the range of possible values of x by combining the two inequalities. We will rewrite x>2 as 2

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Exercises p.457-462

Exercise 17 Page 459

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