Question

Classify each pair of angles as alternate interior, same side interior or corresponding angles

and

Short answer

and are alternate interior angles.

Step-by-step solution

Step 1. Observe the diagram

In the diagram the angles are mentioned by the alphabets A, B, C, D, E, F, G, H, J, K, L respectively.

Step 2. State the definition

Alternate interior angles: These are the two nonadjacent interior angles which are on the opposite sides of the transversal.

Same-side interior angles: These are the two interior angles which are on the same sides of the transversal.

Corresponding angles: These are the two angles which relative to the two lines are in the corresponding position.

Step 3. State the explanation

Consider the figure

It can be observed that $\angle FCB\text{and}\angle CBL$are two nonadjacent interior angles which are on the opposite sides of the transversal $\overleftrightarrow{BC}$.

Thus, by using the above definitions, it can be said that $\angle FCB\text{and}\angle CBL$are alternate interior angles.