Question

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

If $\angle 2\cong \angle 3$then $AD\left|\right|BC$.

Short answer

Theorem 3 – 5 is used to justify the above statement.

Step-by-step solution

Step 1. Observe that angle ∠2 and ∠3 are alternate interior angles.

From the figure, it can be observed that the angles∠2and∠3are the alternate interior angles which are formed when the lines $\overleftrightarrow{AD}$ and$\overleftrightarrow{BC}$are cut by the transversal $\overleftrightarrow{DB}$ .

Step 2. Determine the theorem or postulate that can be used.

Theorem 3 – 5 states that if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Step 3. Apply the theorem.

Since $\angle 2\cong \angle 3$, so by the theorem 3 – 5, it can be said that the lines $\overleftrightarrow{AD}$ and$\overleftrightarrow{BC}$are parallel.

That is, $\overleftrightarrow{AD}\left|\right|\overleftrightarrow{BC}$.