Lesson: Geometry - 12
Triangles: The Side-Angle Relationship
[Page 12 of 30]
In a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle. Every equilateral triangle is equiangular and every equiangular triangle is equilateral. In a scalene triangle, all the sides have different lengths and all the interior angles have different measures.
The length of a side of a triangle
is proportionate to the degree measurement of its opposite angle.
In ? ABC below, we know that BC > AC > AB.
How do we know this? Well, ? A
is the largest angle, so the side opposite it, BC, must be the
longest side. ? B is the next largest, so the side opposite it, AC, must be the longest.
And ? C is smallest, so AB must be the shortest side.
Triangles in which
two of the angles (and therefore two of the sides) are of equal length
are known as isosceles triangles.
In isosceles ? ABC
in the diagram below, AB = BC.
A triangle in which all three
angles (and therefore all three sides) are of equal measure is known
as an equilateral triangle. In an equilateral triangle, all three
interior angles equal 60°.
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