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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 5 Page 448

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

Statements
Reasons
1.
XW≅ YW
1.
Given
2.
XW = YW
2.
Definition of congruent segments
3.
YZ+ZW > YW
3.
Triangle Inequality Theorem
4.
YZ+ZW > XW
4.
Substitution
Practice makes perfect

Let's begin by marking the congruent segments and coloring some segments in the given diagram.

Since XW≅ YW, we have that XW= YW. Next, by applying the Triangle Inequality Theorem to △ WYZ we obtain three inequalities. YZ + ZW &> YW YZ + YW &> ZW YW + ZW &> YZ Finally, by substituting XW= YW into the first inequality we will get what we wanted to prove. YZ + ZW > XW We will summarize this proof in the following two-column table.

Statements
Reasons
1.
XW≅ YW
1.
Given
2.
XW = YW
2.
Definition of congruent segments
3.
YZ+ZW > YW
3.
Triangle Inequality Theorem
4.
YZ+ZW > XW
4.
Substitution

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arrow_right Exercises p.448-452
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Exercises 2 (Page 448)
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Exercises 6 (Page 449)
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