Question

write an inequality relating the given side lengths. if possible.
vw and ab
choose the correct conclusion below.
a. vw<ab
b. vw=ab
c. vw>ab
d. no conclusion

Explanation:

Step1: Recall the Hinge Theorem

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is smaller than the included angle of the second triangle, then the third side of the first triangle is shorter than the third side of the second triangle.
In \(\triangle VWU\) and \(\triangle ABC\), \(VU = AC\) and \(WU=BC\) (marked as equal). The included angle in \(\triangle VWU\) is \(45^{\circ}\), and the included angle in \(\triangle ABC\) is \(68^{\circ}\). Since \(45^{\circ}<68^{\circ}\).

Step2: Apply the Hinge Theorem

By the Hinge Theorem, if \(a = a\), \(b = b\) (two pairs of equal sides) and \(\theta_1<\theta_2\) (included angles), then \(c_1 < c_2\). Here, \(VW\) is the side opposite the \(45^{\circ}\) angle and \(AB\) is the side opposite the \(68^{\circ}\) angle. So \(VW

Answer:

A. \(VW < AB\)