Hinge Theorem

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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 one triangle congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

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CCSS.HSG.CO.C.10

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CCSS.7.G.B.5

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CCSS.HSG.CO.C.10

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It means that the length of segment RT is greater than the length of segment VX.

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What does it mean if two angles are congruent?

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Two angles are congruent if they have the same measure.

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CCSS.8.G.A.2

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CCSS.HSG.CO.C.10

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What is the relationship between angles and sides in a triangle according to the Hinge Theorem?

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In a triangle, larger angles are opposite longer sides.

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CCSS.2.G.A.1

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

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The included angle is crucial because it determines the relationship between the lengths of the opposite sides.

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CCSS.HSG.CO.B.7