5.5. Altitudes http://www.ck12.org
5.5 Altitudes
Here you’ll learn the definition of altitude and how to determine where a triangle’s altitude will be found.
What if you were given one or more of a triangle’s angle measures? How would you determine where the triangle’s
altitude would be found? After completing this Concept, you’ll be able to answer this type of question.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter5AltitudesA
MEDIA
Click image to the left for more content.James Sousa:Altitudes of a Triangle
Guidance
Analtitudeis a line segment in a triangle from a vertex and perpendicular to the opposite side, it is also known as
the height of a triangle. All of the red lines are examples of altitudes:
As you can see, an altitude can be a side of a triangle or outside of the triangle. When a triangle is a right triangle,
the altitude, or height, is the leg. To construct an altitude, construct a perpendicular line through a point not on the
given line. Think of the vertex as the point and the given line as the opposite side.
Investigation: Constructing an Altitude for an Obtuse Triangle
Tools Needed: pencil, paper, compass, ruler
- Draw an obtuse triangle. Label it 4 ABC, like the picture to the right. Extend sideAC, beyond pointA.
- Construct a perpendicular line toAC, throughB.
The altitude does not have to extend past sideAC, as it does in the picture. Technically the height is only the vertical
distance from the highest vertex to the opposite side.
As was true with perpendicular bisectors, angle bisectors, and medians,the altitudes of a triangle are also concurrent.
Unlike the other three, the point does not have any special properties.