Q12. In the diagram for Exercise 11, ... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q12. (page 112)

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

Short Answer

Expert verified

$E B$ and $D F$ 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 $鈭� E B C$ and $鈭� 2$ are equal in measure and they form a pair of alternate angles which implies that $E B$ and $D F$ are parallel to each other.

Step 2. Description of step.

From the given figure it can be observed that $鈭� 1$ and $鈭� 2$ are equal in measure and they form a pair of same side interior angles which implies that $E B$ and $D F$ are parallel to each other.

Step 3. Description of step.

From the given figure it can be observed that $鈭� 3$ and $鈭� 5$ are equal in measure and they form a pair of corresponding angles which implies that $E B$ and $D F$ are parallel to each other.

Therefore, $E B$ and $D F$ are parallel to each other because they form a pair of alternate interior angles, same side interior angles and corresponding angles.