Question

Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of angles. What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning? A. When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent. B. When a pair of parallel lines are intersected by a third line, the alternate interior angles are acute. C. When a pair of parallel lines are intersected by a third line, all of the angles formed are obtuse. D. When a pair of parallel lines are intersected by a third line, all of the angles formed are congruent.

Answer 1

The only correct statement among the choices is:

A. When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.

 

This statement can actually be proven by measuring the angles of the alternate interior angles. We can actually see that they have equal measurements. While the adjacent interior angles are supplementary angles.