Relationship of sides to interior angles in a triangle

In any triangle:
  1. The shortest side is always opposite the smallest interior angle
  2. The longest side is always opposite the largest interior angle
Try this Drag the orange dots on the triangle below.

Recall that in a scalene triangle, all the sides have different lengths and all the interior angles have different measures. In such a triangle, the shortest side is always opposite the smallest angle. (These are shown in bold color above) Similarly, the longest side is opposite the largest angle.

In the figure above, drag any vertex of the triangle and see that whichever side is the shortest, the opposite angle is also the smallest. Then click on 'show largest' and see that however you reshape the triangle, the longest side is always opposite the largest interior angle.

The mid-size parts

If the smallest side is opposite the smallest angle, and the longest is opposite the largest angle, then it follows that since a triangle only has three sides, the midsize side is opposite the midsize angle.

Equilateral triangles

An equilateral triangle has all sides equal in length and all interior angles equal. Therefore there is no "largest" or "smallest" in this case.

Isosceles triangles

Isosceles triangles have two sides the same length and two equal interior angles. Therefore there can be two sides and angles that can be the "largest" or the "smallest". If you are careful with the mouse you can create this situation in the figure above.

Other triangle topics


Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises