Question

Complete: If $\overline{AE}||\overline{BD}$then $\angle 1\cong$ and$\angle 9\cong$ .

Short answer

The first blank should be filled with $\mathbf{\angle }\mathbf{4}$and second blank should be filled with $\mathbf{\angle }\mathbf{3}$.

Step-by-step solution

Step 1. Observe the provided information

The provided two parallel lines are having two separate lines $\overline{AB}$and $\overline{EB}$that are travelling through them.

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

The postulate 10 can be used which states that two angles represents the corresponding angles only when a separate line travels through these two lines which are having a parallel relation between them.

The theorem 3-2 can be used which states that if two lines are having a separate line that is traveling through them then the angles are congruent which are positioned on alternate interior side of the lines.

Step 3. Determine the angles that are congruent

According to the travelling line $\overline{AB}$and postulate 10, the congruent angles are,

$\angle 1\cong \angle 4$

According to the travelling line role="math" localid="1637836897205" $\overline{EB}$and theorem 3-2, the congruent angles are,

Step 4. Make the conclusion

According to the obtained congruent angles the first blank should be filled with $\angle 4$and second with $\angle 3$.