Answer:
- The answer shown in you picture is wrong. The correct answer is the first one: Hinge Theorem.
Explanation:
To answer this question let's check the hinge theorem:
This theorem permits to compare the length of two sides (the "third sides") of two triangles, given that two pairs of sides are known to be congruent and the included angles are different.
The theorem states that when two sides of a triangle are congruent to two sides of another triangle and the included angle of the two sides of the first triangle is greater than the included angle of the sides of the second triangle, then the third side of the first triangle is larger than the third side of the second triangle.
In this case we want to compare sides TU and SV.
TU is "the third side" of the triangle UVT, and SV is the "third side" fo the triangle STV.
It is given that sides ST and VU are congruent.
By reflective property side TV, of triangle STV, is congruent to side TV of triangle UVT.
Hence, you have that two pairs of sides are congruent.
Now, you compare the angles STV and TVU: angle STV measures 44º and angle TVU measures 45º.
Hence, you can use directly the HInge Theorem to conclude that side TU is greater than side SV.
