Answer:
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- <u>The correct answer is the first choice: Hinge Theorem.</u>
Explanation:
The <em>Hinge Theorem</em> compares the lengths of two sides of two triangles, given that the other two pairs of sides are congruent and the included angles are different.
The theorem states that if two sides of a triangle are congruent to two sides of another triangle and the included angle of one triangle is greater than the included angle of the other triangle, then length of the third side of the first triangle is greater than the length of the third side of the second triangle.
The figures shows triangles UVT and STV
The angle UVT is greater than the angle STV.
The sides ST and VU are congruent, as the small vertical marks indicate.
The side TV is a common side of both triangles.
Then, you already have that two sides of the triangle STV are congruent to two sides of triangle UVT and the angle UVT is greater than the angle STV.
Hence, by the HInge Theorem the side TU is greater than side SV.
