Let's analyze each statement based on the diagram:

Diagram observations:

• We have two parallel lines cut by a transversal. The angles formed by this setup follow specific relationships.

Statement-by-statement analysis:

A. $\angle 3 \cong \angle 2$ because they are alternate interior angles.

• $\angle 3$ and $\angle 2$ are not alternate interior angles. Alternate interior angles occur between the two parallel lines on opposite sides of the transversal. In this case, $\angle 3$ and $\angle 2$ are adjacent, so this is false.

B. $m \angle 1 + m \angle 3 = 180^\circ$ because they form a straight angle.

• $\angle 1$ and $\angle 3$ are adjacent angles on a straight line, forming a linear pair. Therefore, their measures add up to $180^\circ$. This statement is true.

C. $\angle 3 \cong \angle 6$ because they are alternate interior angles.

• $\angle 3$ and $\angle 6$ are indeed alternate interior angles since they are on opposite sides of the transversal and inside the parallel lines. This statement is true.

D. $\angle 1$ and $\angle 6$ are supplementary because $\angle 3 \cong \angle 6$ and $m \angle 1 + m \angle 3 = 180^\circ$.

• This statement is a bit misleading. While $\angle 1$ and $\angle 3$ are supplementary, $\angle 1$ and $\angle 6$ are not supplementary. So this statement is false.

E. $\angle 1 \cong \angle 3$ because they are vertical angles.

• $\angle 1$ and $\angle 3$ are not vertical angles. Vertical angles are formed by two intersecting lines, but $\angle 1$ and $\angle 3$ are adjacent. This statement is false.

Final conclusion:

• B and C are the true statements.

Would you like further details or clarification on any of the concepts?

Here are 5 related questions for practice:

1. How do you identify alternate interior angles?
2. What is the definition of supplementary angles?
3. What are vertical angles and how do you identify them?
4. Why are $\angle 3$ and $\angle 6$ congruent?
5. Can two adjacent angles ever be congruent? Why or why not?

Tip: Always remember that alternate interior angles are formed between two parallel lines and are congruent when a transversal crosses them.