Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 7 - Section 7.2 - Concurrence of Lines - Exercises - Page 325: 10

Answer

(a) To locate the orthocenter, it is not necessary to construct all three altitudes of a right triangle. (b) The orthocenter of a right triangle is the vertex with the right angle.
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Work Step by Step

(a) To locate the orthocenter, it is not necessary to construct all three altitudes of a right triangle. (b) An altitude is a perpendicular line from a vertex of a triangle to the opposite side. The orthocenter is the point where the three altitudes of a triangle intersect. In the sketch, the altitude of vertex A is the line $AC$, and the altitude of vertex B is the line $BC$. Note that these two altitudes intersect at the point C. Also, the altitude of vertex C obviously includes the point C. Therefore, the orthocenter of any right triangle is the vertex with the right angle.
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