An arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to the other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Draw the figure and explain why the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.
An arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to the other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Draw the figure and explain why the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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An arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to the other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Draw the figure and explain why the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.
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