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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. Inequalities in Two Triangles
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Exercise 9 Page 458

Use the Converse of the Hinge Theorem.

Statements
Reasons
1.
AD ≅ CB
1.
Given
2.
BD ≅ BD
2.
Reflexive Property of Congruent Segments
3.
DC < AB
3.
Given
4.
m∠ CBD < m∠ ADB
4.
Converse of the Hinge Theorem
Practice makes perfect

Let's begin by highlighting the congruent parts and adding some colors to the given diagram.

By the Reflexive Property of Congruent Segments we have that BD ≅ BD. Therefore, by applying the Converse of the Hinge Theorem we have that m∠ CBD < m∠ ADB.

Two-Column Proof

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

Statements
Reasons
1.
AD ≅ CB
1.
Given
2.
BD ≅ BD
2.
Reflexive Property of Congruent Segments
3.
DC < AB
3.
Given
4.
m∠ CBD < m∠ ADB
4.
Converse of the Hinge Theorem
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arrow_right Exercises p.457-462
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Exercises 2 (Page 457)
Exercises 3 (Page 457)
Exercises 4 (Page 457)
Exercises 5 (Page 458)
Exercises 6 (Page 458)
Exercises 7 (Page 458)
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Exercises 9 (Page 458)
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Exercises 28 (Page 460) engineering
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Exercises 39 (Page 461) engineering
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