The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
The altitude of a triangle is the perpendicular line which joins one vertex of a triangle to a point on the opposite side. (A line joining the vertex to an arbitrary point is called a cevian.) Each acute triangle has exactly three altitudes. The three altitudes of such a triangle always meet at a central point known as the orthocenter. Obtuse and right triangles also have altitudes. However, for a right triangle, one of the legs is an altitude, and the orthocenter lies along the edge of the triangle. For obtuse triangles, the sides must be extended a certain distance to allow for a perpendicular to be formed. In this case, the orthocenter will lie outside the triangle itself.
The altitude is most commonly used in calculations of the area of a triangle: the area can be found by halving the product of a side with the altitude perpendicular to that side. The altitude can also be calculated indirectly if one already knows the area or if one knows the lengths of all the sides (from which Heron's formula is used to calculate the area; see Hero's formula). The altitude is among the geometric properties commonly used in proofs and theorems, as well as in construction of figures using compass and straightedge.