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Consider Theorem 5.9 about Angle-Side Relationships in Triangles.
Angles: ∠ A, ∠ C, ∠ B
Sides: BC, AB, AC
To find the order of the angle measures and sides from smallest to largest, let's look at the given diagram and notice the marked lengths of the sides.
BC< AB< AC ⇕ 1.7 < 2.8 < 3.1 Next, let's consider Theorem 5.9 about Angle-Side Relationships in Triangles.
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Angle-Side Relationships in Triangles |
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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. |
Now we need to think about the sides, and the corresponding opposite angles. cc Side & Opposite Angle [0.5em] BC & ∠ A [0.5em] AB & ∠ C [0.5em] AC & ∠ B Therefore, we can list the angles in order from smallest to largest. m∠ A < m∠ C < m∠ B