Question

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer.

If $\overleftrightarrow{EC}\left|\right|\overleftrightarrow{BD}$ then$\angle 7\cong \_\_$

Short answer

The statement is$\angle 7\cong \angle 1$.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of the alternate interior angle property.

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Step 3- Step description.

Sincefrom the figure the two parallel lines are cut by a transversal thus the alternate interior will be congruent such that angle 7 is congruent to angle 1.

Thus, the statement is $m\angle 1\cong m\angle 7$ and the postulate is alternate interior angle property.