Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Section 8.3 - Regular Polygons and Area - Exercises - Page 367: 36

Answer

For starters, there is a set of vertical angles, so we know that a pair of angles in triangles QTF and VRF are congruent by the vertical angles theorem. In addition, since all sides of regular pentagons are congruent, it follows that corresponding sides are also congruent. Finally, we know that corresponding angles are congruent, for all angles in regular pentagons are congruent, so angles evenly divided by the triangles created by the diagonals are also congruent. Thus, QTF and VRS are congruent by ASA. Thus, we obtain: $ \frac{VF}{TF} = \frac{FQ}{FR} \\ VFFR =TFFQ$
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