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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

Subchapter links

Exercises p.457-462