Question

1. select the inequality that relates kl and yz in (\triangle jkl) and (\triangle xyz).

Explanation:

Step1: Apply 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 larger than the included angle of the second triangle, then the side opposite the larger included angle is longer.
In \(\triangle JKL\) and \(\triangle XYZ\), \(JK = XY\) and \(JL = XZ\). The included angle \(\angle J=45^{\circ}\) and the included angle \(\angle X = 30^{\circ}\), and \(45^{\circ}>30^{\circ}\).

Step2: Compare the sides opposite the included angles

Since \(45^{\circ}>30^{\circ}\), by the Hinge Theorem, the side opposite \(\angle J\) (\(KL\)) is longer than the side opposite \(\angle X\) (\(YZ\)).

Answer:

\(KL>YZ\)