Triangle
A triangle is
a figure formed when three
noncollinear points are
connected by segments.
Each
pair of segments forms an angle of the triangle. The vertex of
each angle is a vertex of the
triangle.
The sum of the measures of the angles of a triangle
is 180.
The sum of the lengths of any two sides of a triangle must be greater than the third side. That is:
a + b > c
a + c > b
b + c > a
The subtraction of the lengths of any two sides of a triangle must be smaller than the third side.
Triangles can be classified by:
Their sides:
Equilateral |
Isosceles |
Scalene |
|
|
|
| All three sides have equal lengths |
Exactly two equal sides |
All sides have different lengths |
Their angles:
Acute |
Right |
Obtuse |
|
|
|
All interior angles are acute (<90º) |
One angle is a right angle (90º) |
One angle is obtuse (>90º) |
Area of a triangle
There are several ways to compute the area of a triangle:
1.
When you know the lenght of the base and the height, you can use the formula:
2. Another is Heron's formula which gives the area in terms of the three sides of the triangle:
Suppose we know the values of the three sides
a, b and c of the triangle.
If
s is the semiperimeter of the triangle, that is,
s = (
a +
b +
c)/2, then:
(s-b)(s-c)})
