So, in a triangle, angles opposite equal sides are equal; and conversely, sides opposite equal angles are equal. Thus if in a triangle, two sides are unequal, the angles opposite are unequal; and if two angles are equal, the sides opposite are unequal. But can we say which of the unequals is greater? Might it be that the greater lies opposite the greater? Indeed that is the case. We prove that this is so in Chapter 6 together with a number of other theorems that tells us when something must be greater or less.
6.1 The Anisosceles Triangle Theorem and its Converse
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6.2 The Triangle Inequality
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6.3 The Hinge Theorem and its Converse
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6.4 Optimization - Point to Line, Line to Line
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6.5 Optimization - Point to Circle, Line to Circle, Circle to Circle
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