A triangle is any polygon with three sides.
Triangle Classifications Based On Angles
Right
A right triangle is any triangle with an angle of 90°.
Special Right Triangles
45-45-90
A 45-45-90 triangle is a triangle whose angles measure only 90° and 45°. Shortcuts to finding the lengths of missing sides can be found here.
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so therefore,
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30-60-90
A 30-60-90 triangle is a triangle whose angles measure only 30°, 60°, and 90°. Shortcuts to finding the lengths of missing sides can be found here.
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so therefore,
- , or
Acute
An acute triangle is any triangle where all the angles measure less than 90°.
Equiangular
An equiangular triangle is an acute triangle in which all sides and angles are the same. The angles in equiangular triangles always measure 60°.
Obtuse
An obtuse triangle is any triangle where one angle measures more than 90°.
Triangle Classification Based On Sides
Equilateral
An equilateral (Latin aequalis "equal" + latus "side") triangle, also called an equiangular triangle, is an acute triangle in which all sides and angles are the same. The angles in equilateral triangles always measure 60°.
Isosceles
An isosceles (Greek ίσος ísos "same" + σκελες skeles "legs") triangle is any triangle where 2 sides are congruent, leaving the base angles congruent as well.
Scalene
A scalene triangle is any triangle where no sides are congruent.