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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Inequalities in One Triangle

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Exercise 31 Page 431

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

m∠ BCF > m∠ CFB

Practice makes perfect

We are asked to determine the relationship between ∠ BCF and ∠ CFB. 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 ∠ BCF is opposite to FB and ∠ CFB is opposite to BC. We are given the measurements for these segment lengths. FB&=15 [0.5em] BC&=14 Because FB is longer than BC, by the theorem, m∠ BCF is greater than m∠ CFB. m∠ BCF > m∠ CFB

Subchapter links

Exercises p.430-433