In this diagram, we have two parallel lines $g$ and $h$ that are intersected by a transversal $b$. The angles created by these lines are numbered from 1 to 8. You are asked to identify:

1. A pair of alternate exterior angles.
2. A pair of alternate interior angles.
3. A pair of corresponding angles.

Solution:

(a) Alternate exterior angles: These are the angles that are on opposite sides of the transversal $b$ and outside the two parallel lines $g$ and $h$.

• Angle 1 and angle 8 form a pair of alternate exterior angles.

(b) Alternate interior angles: These are the angles that are on opposite sides of the transversal $b$ but inside the two parallel lines $g$ and $h$.

• Angle 3 and angle 5 form a pair of alternate interior angles.

(c) Corresponding angles: These are the angles that are on the same side of the transversal $b$ and in corresponding positions relative to the parallel lines $g$ and $h$.

• Angle 2 and angle 6 form a pair of corresponding angles.

Summary:

• (a) Alternate exterior angles: $\angle 1$ and $\angle 8$
• (b) Alternate interior angles: $\angle 3$ and $\angle 5$
• (c) Corresponding angles: $\angle 2$ and $\angle 6$

Would you like any further details or clarifications?

Here are 5 related questions:

1. Can alternate exterior angles ever be supplementary?
2. How do we determine if two lines are parallel using corresponding angles?
3. What is the sum of the angles on a straight line?
4. Are alternate interior angles always congruent when the lines are parallel?
5. How can we apply these angle relationships in real-world situations?

Tip: Remember, for parallel lines cut by a transversal, alternate interior and corresponding angles are always congruent!