Mark as true any statement that is always true. Mark as false any statement that is never true or that is not necessarily true. Be able to justify your answers.

Question

1. Any set of three lines in the same plane has one pair of parallel lines and one transversal line.
2. To begin an argument using indirect reasoning, we assume that the hypothesis of the statement to be proved is true and that the negation of the conclusion of the statement is true.
3. If two lines cut by a transversal form a pair of supplementary corresponding angles with the transversal, then the lines are parallel.
4. The exterior angle to any vertex in a triangle is equal to the sum of any two interior angles in the triangle.
5. If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

Answer 1

1. F: There are many counterexamples including three parallel lines and three lines with no
parallel relationships.
2. T
3. F: Corresponding angles are congruent if the lines are parallel.
4. F: The two interior angles must be nonadjacent.
5. T