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.

Chapter9: Surfaces And Solids

Section9.2: Pyramids, Area, And Volume

Problem 37E

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