Respuesta :
Answer: Option 'b' is correct.
Step-by-step explanation:
To prove that two lines are parallel when it cut be transversal.
Let m and n are two lines and the lines are cut by transversal k.
Then, if we show that the alternate interior angles are equal, then m and n become parallel to each other.
So, the converse of the alternate interior angles theorem correctly justifies that the lines are parallel when cut by transversal.
Hence, option 'b' is correct.
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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