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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
6. Inequalities in Two Triangles
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Exercise 8 Page 458

Notice that ∠ 1 is an exterior angle to △ WYZ.

Statements
Reasons
1.
△ YZX and YZ ≅ XW
1.
Given
2.
WZ ≅ WZ
2.
Reflexive Property of Congruent Segments
3.
∠ 1 is exterior to △ WYZ
3.
Given
4.
m ∠ 1 > m∠ 2
4.
Exterior Angle Inequality
5.
ZX > YW
5.
Hinge Theorem
Practice makes perfect

Let's start by highlighting the congruent parts in the given diagram.

By the Reflexive Property of Congruent Segments we have that WZ ≅ WZ. Also, we can see that ∠ 1 is an exterior angle to △ WYZ.

Therefore, by the Exterior Angle Inequality we have that m ∠ 1 > m ∠ 2. Consequently, by the Hinge Theorem we have that ZX > YW.

Two-Column Proof

In the following table we will summarize the proof we did before.

Statements
Reasons
1.
△ YZX and YZ ≅ XW
1.
Given
2.
WZ ≅ WZ
2.
Reflexive Property of Congruent Segments
3.
∠ 1 is exterior to △ WYZ
3.
Given
4.
m ∠ 1 > m∠ 2
4.
Exterior Angle Inequality
5.
ZX > YW
5.
Hinge Theorem
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Exercises 2 (Page 457)
Exercises 3 (Page 457)
Exercises 4 (Page 457)
Exercises 5 (Page 458)
Exercises 6 (Page 458)
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Exercises 8 (Page 458)
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