Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
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Chapter 7 - Section 7.2 - Concurrence of Lines - Exercises - Page 326: 43

Answer

$\angle FOA$ and $\angle BOC$ are supplementary.

Work Step by Step

Using the result from Exercise 42, we can state the following: $\triangle AOF \cong \triangle AOE$ By a similar argument: $\triangle BOF \cong \triangle BOD$ $\triangle DOC \cong \triangle EOC$ Therefore: $\angle FOA \cong \angle EOA$ $\angle BOF \cong \angle BOD$ $\angle DOC \cong \angle EOC$ Then: $\angle FOA + \angle EOA +\angle BOF + \angle BOD + \angle DOC + \angle EOC = 360^{\circ}$ $\angle FOA + \angle FOA +\angle BOD + \angle BOD + \angle DOC + \angle DOC = 360^{\circ}$ $2\angle FOA +2\angle BOD + 2\angle DOC = 360^{\circ}$ $\angle FOA +\angle BOD + \angle DOC = 180^{\circ}$ $\angle FOA +\angle BOC = 180^{\circ}$ Therefore, $\angle FOA$ and $\angle BOC$ are supplementary.
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