​Altitudes of a Triangle

About Geometry Worksheet Assignment 3.16:     

 

Assignment 3.16 is an introduction to the altitudes of a triangle.

 

Prerequisite Skills: Identify vertices of triangles (Assignment 3.1).  Identify perpendicular lines (Assignment 2.16).  Draw lines from a point perpendicular a line (Assignment 2.19).  Name line segments (Assignment 1.12). 

 

Definition:  An altitude of a triangle is a line segment perpendicular to a side of the triangle with one endpoint on the line containing the side and the other endpoint

                        at a vertex.

 

Theorems:  In an acute triangle, each altitude lies in the interior of the triangle.

 

                         In a right triangle, the altitudes from the vertices of the acute angles are legs of the triangle and the altitude from the vertex of the right angle lies in

                         the interior of the triangle. 

 

                        In an obtuse triangle, the altitudes from the vertices of the acute angles lie in the exterior of the triangle and the altitude from the vertex of the obtuse

                        angle lies in the interior of the triangle.