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McGraw Hill Glencoe Geometry, 2012

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McGraw Hill Glencoe Geometry, 2012 View details

3. Inequalities in One Triangle

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Exercise 32 Page 349

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

m∠ BFD < m∠ BDF

Practice makes perfect

We are asked to determine the relationship between ∠ BFD and ∠ BDF. 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 ∠ BFD is opposite to DB and ∠ BDF is opposite to BF. We are given the measurements for these segment lengths. DB&=12 [0.5em] BF&=15 Because DB is shorter than BF, by the theorem, m∠ BFD is less than m∠ BDF. m∠ BFD < m∠ BDF

Subchapter links

Check Your Understanding p.348

Practice and Problem Solving p.348-350

H.O.T. Problems p.350

Standardized Test Practice p.351

Spiral Review p.351

Skills Review p.351