Relationship of sides to interior angles in a triangle
In a triangle:
 The shortest side is always opposite the smallest
interior angle
 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 midsize 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.
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Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
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