Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 2 - Section 2.2 - Indirect Proof - Exercises - Page 81: 25

Answer

$\mathbb{ASSUME}$ that $\overrightarrow{\rm FH}$ $\bot$ $\overleftrightarrow{\rm EG}$. Then $\angle$3 $\cong$ $\angle$4 and m$\angle$3 $=$ m$\angle$4. But it is given that m$\angle$3 $\gt$ m$\angle$4, which leads to a contradiction. Then the assumption $\overrightarrow{\rm FH}$ $\bot$ $\overleftrightarrow{\rm EG}$ must be false and it follows that $\overrightarrow{\rm FH}$ is not perpendicular to $\overleftrightarrow{\rm EG}$.

Work Step by Step

Work cannot be shown for a proof. Logic is the only work done in such instances. Such work takes place mentally, and therefore cannot be shown.
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