Question

Looking at the parallel lines which conjecture is reasonable to make? (See attachment)

Answer 1

In this case B. would be the most reasonable conjecture, because is the only option that accurately describes all three examples in the picture.

The first option is incorrect: This is because 'supplementary' means the angles add up to 180º, but none of the pairs of alternate exterior angles in the picture add up to 180º. This is also false because alternate interior angles formed by two parallel lines and a third line are supposed to be congruent not supplementary.

The second option is correct: The alternate interior angles formed by two parallel lines and a third line are indeed congruent. The examples in the picture all fit with that statement.

The third option is incorrect: Although this may be true some of the time the alternate interior angles don't necessarily have to be obtuse (bigger than 90º). One of the examples in the picture shows a pair of alternate interior angles each with a measure of 45º, an acute angle (less than 90º), showing that alternate interior angles aren't only obtuse, they can be acute also.

The fourth option is also incorrect: This conjecture isn't always true because not all the angles formed are congruent. This conjecture is only true when the third line intercepts the parallel lines perpendicularly.