Exercise 49 Page 314

We are given a series of statements and we must determine which are true. Let's go through each statement and see.

Statement I

The first statement is the following. Let's begin with reviewing that alternate interior angles are nonadjacent interior angles that lie on opposite sides of the transversal. We can examine the given diagram and see if $\angle 3$ and $\angle 6$ meet this definition.

As we can see, these are interior angles that lie on opposite sides of the transversal $t.$ Thus, $\angle 3$ and $\angle 6$ are indeed Alternate Interior Angles. The statement is true.

Statement II

The second statement is as follows. Let's recall that consecutive interior angles are interior angles that lie on the same side of the transversal. Do $\angle 4$ and $\angle 6$ meet this definition? Let's see.

These angles lie in the region between lines $m$ and $n,$ so they are interior angles. Moreover, they lie on the same bottom side of the transversal $t.$ Therefore, the statement is true and $\angle 4$ and $\angle 6$ are indeed Consecutive Interior Angles.

Statement III

Finally, the third statement is the following. Alternate exterior angles are nonadjacent exterior angles that lie on opposite sides of the transversal. Let's analyze the given diagram and see if $\angle 1$ and $\angle 7$ can be described as such.

We can see that the angles lie in the two regions that are not between the lines $m$ and $n.$ Thus, they are exterior angles. However, they lie on the same, not opposite, side. This means they are not Alternate Exterior Angles. The statement is false.