CK-12 Geometry-Concepts

5.5. Altitudes http://www.ck12.org

In a right triangle, the altitude, or the height, is the leg. If we rotate the triangle so that the right angle is in the lower
left corner, we see that legBCis an altitude.

Example B

A triangle has angles that measure 55◦, 60 ◦,and 65◦. Where will the orthocenter be found?

Because all of the angle measures are less than 90◦, the triangle is an acute triangle. The orthocenter of any acute
triangle is inside the triangle.

Example C

A triangle has an angle that measures 95◦. Where will the orthocenter be found?

Because 95◦> 90 ◦, the triangle is an obtuse triangle. The orthocenter will be outside the triangle.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52539

CK-12 Foundation: Chapter5AltitudesB

Vocabulary

Thealtitudeof a triangle, also known as the height, is a line segment from a vertex and perpendicular to the opposite
side. Perpendicularlines are lines that meet at right (90◦) angles. Theorthocenterof a triangle is the point of
concurrency for the altitudes of triangle (the point where all of the altitudes meet).

Guided Practice

1. True or false: The altitudes of an obtuse triangle are inside the triangle.


2. Draw the altitude for the triangle shown.