By internal angles
Triangles can also be classified according to their , measured here in .
- A right triangle (or right-angled triangle, formerly
called a rectangled triangle) has one of its interior angles
measuring 90° (a ). The side opposite to the right angle is
the ;
it is the longest side of the right triangle. The other two sides are
called the legs or catheti
(singular: ) of the
triangle. Right triangles obey the : the sum of the
squares of the lengths of the two legs is equal to the square of the
length of the hypotenuse: a2 + b2 = c2,
where a and b are the lengths of the legs and c is
the length of the hypotenuse. are right
triangles with additional properties that make calculations involving
them easier. The most famous is the 3-4-5 right triangle, where 32
+ 42 = 52. In this situation, 3, 4,
and 5 are a .
- Triangles that do not have an angle that measures 90° are called oblique
triangles.
- A triangle that has all interior angles measuring less than 90° is
an acute triangle or acute-angled triangle.
- A triangle that has one angle that measures more than 90° is an obtuse
triangle or obtuse-angled triangle.
A triangle that has two angles with the same measure also has two
sides with the same length, and therefore it is an isosceles triangle.
It follows that in a triangle where all angles have the same measure,
all three sides have the same length, and therefore such triangle is
equilateral.
![Right triangle]() |
![Obtuse triangle]() |
 |
| Right |
Obtuse |
Acute |
| |
![\underbrace{\qquad
\qquad \qquad \qquad \qquad \qquad}_{}]() |
| |
Oblique |
By
relative lengths of sides
Triangles can be classified according to the relative lengths of
their sides:
- In an equilateral triangle all sides have the same length. An
equilateral triangle is also a with all angles measuring 60°.
- In an isosceles triangle, two sides are equal in length.
An isosceles triangle also has two angles of the same measure; namely,
the angles opposite to the two sides of the same length; this fact is
the content of the . Some
mathematicians define an isosceles triangles to have only two equal
sides, whereas others define that an isosceles triangle is one with at
least two equal sides.
The latter definition would make all equilateral triangles isosceles
triangles.
- In a scalene triangle, all sides are unequal.
The three angles are also all different in measure. Notice that a
scalene triangle can be (but need not be) a right triangle.
.
![Equilateral
Triangle]() |
![Isosceles triangle]() |
![Scalene triangle]() |
| Equilateral |
Isosceles |
Scalene |
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