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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. The Triangle Inequality
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Exercise 19 Page 449

Apply the Triangle Inequality Theorem to â–³ JKL and use the appropriate inequality.

Statements
Reasons
1.
JL ≅ LM
1.
Given
2.
JL = LM
2.
Definition of congruent segments
3.
KJ + KL > LJ
3.
Triangle Inequality Theorem
4.
KJ + KL > LM
4.
Substitution
Practice makes perfect

Let's highlight the congruent segments in the given diagram and color â–³ JKL.

By applying the Triangle Inequality Theorem to △ JKL, we obtain three inequalities. KJ + KL &> JL KJ + JL &> KL KL + JL &> KJ Since JL ≅ LM, we have that JL = LM. By substituting it into the first inequality above we will get the desired result. KJ + KL > LM Let's summarize this proof in the following two-column table.

Statements
Reasons
1.
JL ≅ LM
1.
Given
2.
JL = LM
2.
Definition of congruent segments
3.
KJ + KL > LJ
3.
Triangle Inequality Theorem
4.
KJ + KL > LM
4.
Substitution

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arrow_right Exercises p.448-452
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Exercises 2 (Page 448)
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