Hinge Theorem & Converse

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What is the Hinge Theorem?

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The Hinge Theorem states that if two triangles have two sides of equal length and the included angle of one triangle is larger than the included angle of the other, then the side opposite the larger angle is longer than the side opposite the smaller angle.

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What is the Converse of the Hinge Theorem?

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The Converse of the Hinge Theorem states that if two triangles have two sides of equal length and the side opposite one angle is longer than the side opposite another angle, then the angle opposite the longer side is larger than the angle opposite the shorter side.

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This inequality represents all real numbers between -20 and 21, not including -20 and 21.

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What is the significance of the included angle in the Hinge Theorem?

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The included angle determines the relationship between the lengths of the opposite sides in the triangles being compared.

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