Acute Triangle
From Latin: acutus  "sharp, pointed"
A triangle where all three internal angles are
acute (less than 90 degrees).
Try this Drag the orange dots on each vertex to reshape the triangle.
If any angle becomes 90 degrees or more, it is not an acute triangle.
In any triangle, two of the interior angles are always
acute (less than 90 degrees)^{*},
so there are three possibilities for the third angle:
 Less than 90°  all three angles are acute and so the triangle is acute.
 Exactly 90°  it is a
right triangle
 Greater than 90° (obtuse): the triangle is an
obtuse triangle
In the figure above, drag the vertices around and try to create all 3 possibilities. The title will change to reflect the type of triangle you have created. (You may have to move the mouse slowly to get an angle to be exactly 90°).
* To see why this is so: The internal angles of any triangle always add up to 180°.
If two angles were greater than 90° they would add to more then 180° just by themselves. Therefore this can never happen.
(Prove it to yourself  reshape the triangle above and try to get two angles to be greater than 90°).
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
(C) 2009 Copyright Math Open Reference. All rights reserved
