Question

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

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 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 \(\triangle LKM\) and \(\triangle ACB\), two pairs of sides are equal (\(LK = AC\) and \(KM=CB\)). The included angle in \(\triangle LKM\) is \(42^{\circ}\), and the included angle in \(\triangle ACB\) is \(60^{\circ}\). Since \(42^{\circ}<60^{\circ}\).

Step2: Conclude the relationship between \(LM\) and \(AB\)

By the Hinge Theorem, \(LM < AB\).

Answer:

B. \(LM < AB\)