Question

applying the hinge theorem
given ac = ln and ba = ml, which statement must be true?
bc < mn
bc > mn
bc = mn
ba = ln

Explanation:

Step1: Recall Hinge - Theorem

The Hinge - Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Step2: Identify given information

We are given that \(AC = LN\), \(BA=ML\), and \(\angle A = 58^{\circ}\), \(\angle L=78^{\circ}\). Since \(\angle L>\angle A\).

Step3: Apply the Hinge - Theorem

By the Hinge - Theorem, the side opposite \(\angle L\) (which is \(MN\)) is longer than the side opposite \(\angle A\) (which is \(BC\)). So \(BC < MN\).

Answer:

BC < MN