Theory:

Right Angle triangle: A triangle where one of its interior angles is a right angle \(90°\).
Right angle triangle_2.png
  
Area:
(Area\) \(A = \) \(1/2(b × h)\)
Thus, height of triangle \(h =\) \(Area × 2 / b\)
And, base of triangle \(b =\) \(Area × 2 / h\)
where \(h\) is denoted as height.
where \(b\) is denoted as base.
 
Perimeter:
\(a²\) \(+\) \(b²\) \( = c²\)
\(a\), \(b\)  are the lengths of the other two sides.
where \(c\) is the length of the hypotenuse.
 
Sides: 
  • The two sides that are not the hypotenuse.
  • They are the two sides making up the right angle itself.
Hypotenuse:
  • The side opposite the right angle.
  • This will always be the longest side of a right triangle. 
Properties:
  • If the two sides that include the right angle are equal in length(\(AB\) and \(BC\)). then it said to be an isosceles triangle.  
  • The hypotenuse (the side opposite the right angle) is always longer than either of the other two sides.so it can never be an equilateral triangle.
Isosceles triangle: A triangle which has two of its sides equal in length.
 
Ascsa.png
  
Area:
\(Area\) \(A = \) \(1/2(b × h)\)
Thus, height of triangle \(h =\) \(Area × 2 / b\)
And, base of triangle \(b =\) \(Area × 2 / h\)
where \(h\) is denoted as height.
where \(b\) is denoted as base.
 
Perimeter:
\(P =\) \(2a + b\)
\(a\) are the lengths of the two equal sides
\(b\)  are the lengths of the other sides.
 
Properties:
  • The 'base' of the triangle is referred to the unequal side of an isosceles triangle.
  • The base angles of an isosceles triangle are always equal. (\(∠ABC\) and \(∠ACB\) are always the same)
  • The altitude is a perpendicular distance from the base to the topmost vertex.
    Important!
  • When the \(3rd\) angle is a right angle, it is called a "right isosceles triangle".
  • If all three sides are the same length it is called an equilateral triangle. Obviously all equilateral triangles also have all the properties of an isosceles triangle.
Equilateral Triangle: A triangle which has all three of its sides equal in length.
 
Cdfd.png
  
Area:
\( Area\) \(A = √3/4\)\( s² \)
where \(s² \) denotes sides of the triangle.
 
Perimeter:
\(perimeter\) \(P = a + b + c \) or \(P = s + s + s\)
\(a\), \(b\), \(c\)  are the lengths of the three equal sides.
or
\(s\)  are the lengths of the three equal sides.
 
Properties:
  • All three angles of an equilateral triangle are always \(60°\).Hence, \(∠ABC\), \(∠CAB\) 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 \(60°\).
  • An equilateral triangle is one in which all three sides are congruent (same length). Because it also has the property that all three interior angles are equal.