4By 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 regular polygon with all angles measuring 60°.
5In an isosceles triangle, two sides are equal in length 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.
6In a scalene triangle, all sides and angles are different from one another.
7By internal anglesA right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle. The other two sides are the legs or catheti (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: 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. Special right triangles are right triangles with additional properties that make calculations involving them easier.
8A triangle that has all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.
9A triangle that has one angle that measures more than 90° is an obtuse triangle or obtuse-angled triangle.
11Area of a triangle The area is half of the base times height. "b" is the distance along the base"h" is the height (measured at right angles to the base)Area = ½bh
12Another way of writing the formula is bh/2 Example: What is the area of this triangle? Height = h = 12 Base = b = 20 Area = bh/2 = 20 × 12 / 2 = 120
13Why is the Area "Half of bh"? Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (it would be a "parallelogram" actually), Then the whole area would be bh (that would be for both triangles, so just one is ½bh), like this: You can also see that if you sliced the new triangle and placed the sliced part on the other side you get a simple rectangle, whose area is bh.