Exercise 33 Page 431

Use the theorem regarding Angle-Side Relationships in Triangles to compare the lengths of the sides opposite to the angles.

m∠ DBF < m∠ BFD

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We are asked to determine the relationship between ∠ DBF and ∠ BFD. Let's consider the given diagram.

In order to compare the angles, we are going to use Theorem 5.9 about Angle-Side Relationships in Triangles.

Angle-Side Relationships in Triangles
If one side of a triangle is longer than another side, then the angle opposite the longer side has greater measure than the angle opposite the shorter side.

From the diagram, we can see that ∠ DBF is opposite to FD and ∠ BFD is opposite to DB. We are given the measurements for these segment lengths. FD&=5 [0.5em] DB&=12 Because FD is shorter than DB, by the theorem, m∠ DBF is less than m∠ BFD. m∠ DBF < m∠ BFD

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Exercises p.430-433

Exercise 33 Page 431

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