Which theorem correctly justifies why the lines m and n are parallel when cut by transversal k? a. converse of the corresponding angles theorem b. converse of the alternate interior angles theorem c. converse of the same side interior angles theorem d. converse of the alternate exterior angles theorem

The converse of a statement is given by reversing the (order of the) statements it contains

The option that gives the correct theorem that justifies why lines m and n ae parallel is option b.

b. Converse of the alternate interior angles theorem

The reason the above selected option is correct is as follows:

Question: Please find attached the diagram of the given figure

The description of the diagram of the given diagram is as follows;

Lines m, and n, pointing in the same direction, and line k is the common transversal

Two alternate interior angles that measure 50°, and are therefore, congruent

Required:

The theorem that correctly justifies why the lines m and n are parallel when cut by the transversal k

Solution:

Given that the alternate interior angles formed by the lines m,  n, and k are congruent, we have;

The converse of the alternate interior angles theorem state given that lines  m, and n, which are intersected by the same transversal line k form alternate interior angles that are congruent, then the lines m, and n are congruent

Therefore;

The theorem that correctly justifies why the lines m and n are parallel when cut by transversal k is the converse of the alternate interior angles theorem

Learn more about the angles formed between two parallel lines having a common transversal here:

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