2. Types Of Triangels
There are seven types of triangle, listed
below. Note that a given triangle can be
more than one type at the same time. For
example, a scalene triangle (no sides the
same length) can have one interior angle
90°, making it also a right triangle. This
would be called a "right scalene triangle".
3. properties
Isosceles - Two sides equal
Equilateral - All sides equal
Scalene - No sides equal
Right Triangle - One angle 90°.
Obtuse One angle greater than 90°
Acute All angles less than 90°
4. Terminology
It is usual to name each vertex of a triangle with a
single capital (upper-case) letter. The sides can be
named with a single small (lower case) letter, and
named after the opposite angle. So in the figure
on the right, you can see that side b is opposite
vertex B, side c is opposite vertex C and so on.
Alternatively, the side of a triangle can be thought
of as a line segment joining two vertices. So then
side b would be called AC. This is the form used on
this site because it is consistent across all shapes,
not just triangles.
6. Isosceles Triangle Property
The unequal side of an isosceles triangle is
usually referred to as the 'base' of the triangle.
The base angles of an isosceles triangle are
always equal. In the figure above, the angles
∠ABC and ∠ACB are always the same
When the 3rd angle is a right angle, it is called
a "right isosceles triangle".
The altitude is a perpendicular distance from
the base to the topmost vertex.
7. Equilateral Triangle Property
All three angles of an equilateral triangle are always 60°. In
the figure above, the angles ∠ABC, ∠CAB and ∠ACB are
always the same. Since the angles are the same and the
internal angles of any triangle always add to 180°, each is 60°.
The area of an equilateral triangle can be calculated in the
usual way, but in this special case of an equilateral triangle, it
is also given by the formula:
area of equilateral triangle formula
Calculator
where S is the length of any one side. See Area of an
equilateral triangle.
With an equilateral triangle, the radius of the incircle is exactly
half the radius of the circumcircle.
8. Right Angled Triangle property
A right triangle can also be isosceles if the
two sides that include the right angle are
equal in length.
A right triangle can never be equilateral,
since the hypotenuse (the side opposite
the right angle) is always longer than
either of the other two sides.
9. Scalene Triangle property
To see why this is so, imagine two angles
are the same. The triangle would then be
an Isosceles triangle, which has two sides
the same length. Similarly, if all three
angles are the same, it would be an
equilateral triangle and all three sides
would be the same length.