Exercise 23 Page 144

Before we consider the pairs of highlighted angles, let's review the definitions of the types of angles pairs that can be formed by a transversal.

• Alternate Interior Angles: Nonadjacent interior angles that lie on opposite sides of the transversal.
• Same-side Interior Angles: Interior angles that lie on the same side of the transversal.
• Corresponding Angles: Angles that lie on the same side of the transversal and in corresponding positions.
• Alternate Exterior Angles: Nonadjacent exterior angles that lie on opposite sides of the transversal.

∠ 1 and ∠ 2

Look at the angles that are labeled ∠ 1 and ∠ 2.

Analyzing them, we can see that ∠ 2 is interior, but ∠ 1 is exterior and they lie on the same side of the transversal. They must be corresponding angles.

∠ 3 and ∠ 4

Now, consider the angles labeled ∠ 3 and ∠ 4.

We see that both ∠ 3 and ∠ 4 are interior and they lie on the same side of the transversal. Therefore, the angles are same-side interior angles.

∠ 5 and ∠ 6

Finally, let's consider the angles labeled ∠ 5 and ∠ 6.

Both angles are interior, but they lie on opposite sides of the transversal. This means that the pair of angles are alternate interior angles.