Relationship of sides to interior angles in a triangle
In a triangle
- The shortest side is always opposite the smallest
- The longest side is always opposite the largest interior angle
Drag the orange dots on the triangle below.
Recall that in a
all the sides have different lengths and all the
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.
An equilateral triangle
has all sides equal in length and all interior angles equal.
Therefore there is no "largest" or "smallest" in this case.
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.
Related triangle topics
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
(C) 2009 Copyright Math Open Reference. All rights reserved