Question

In the diagram for Exercise 11, explain why $\mathit{E}\mathit{B}$and $\mathit{D}\mathit{F}$must be parallel.

Short answer

$EB$ and$DF$ are parallel to each other becausethey form a pair of alternate interior angles, same side interior angles and corresponding angles.

Step-by-step solution

Step 1. Description of step.

From the given figure it can be observed that$\angle EBC$ and$\angle 2$ are equal in measure and they form a pair of alternate angles which implies that$EB$ and$DF$ are parallel to each other.

Step 2. Description of step.

From the given figure it can be observed that$\angle 1$ and$\angle 2$ are equal in measure and they form a pair of same side interior angles which implies that$EB$ and$DF$ are parallel to each other.

Step 3. Description of step.

From the given figure it can be observed that$\angle 3$ and$\angle 5$are equal in measure and they form a pair of corresponding angles which implies that$EB$and$DF$are parallel to each other.

Therefore, $EB$and$DF$are parallel to each other because they form a pair of alternate interior angles, same side interior angles and corresponding angles.