Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

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.

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.