Theory:

Right angle triangle: A triangle where one of its interior angles is a right angle \(90°\).
Right angle triangle.png
 
Area:
  
Area(\(A\)) \(=\) \(1/2(b × h)\).
 
Thus, the height of the triangle(\(h\)) \(=\) Area \(× 2 / b\).
 
And, the base of the triangle(\(b\)) \(=\) Area \(× 2 / h\).
 
Where '\(h\)' is denoted as the height and '\(b\)' is denoted as the base.
 
 
Hypotenuse:  The side opposite to the right angle is named the hypotenuse. It'll always be the longest side of a right triangle
 
 
Sides: The \(2\) sides that aren't the hypotenuse makes the right angle.
  
 
Perimeter:
 
Perimeter(\(P\)) \(=\) \(a + b + c\).
 
The side length of the right triangle are in relation \(a² + b² = c²\)
 
Where '\(a\)', '\(b\)' are the lengths of the other two sides.
 
And '\(c\)' is the length of the hypotenuse.
 
 
Properties:
  • If \(2\) sides which have the right angle are equal in length (\(AB\) and \(BC\)), then it said to be a right isosceles triangle.  
  • The hypotenuse (the side opposite the right angle) is usually longer than either of the other two sides meaning that 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, the height of the triangle(\(h\)) \(=\) Area \(× 2 / b\).
 
And, the base of the triangle(\(b\)) \(=\) Area \(× 2 / h\).
 
Where '\(h\)' is denoted as the height(altitude) and '\(b\)' is denoted as the base.
 
The altitude can be calculated by \(h =\) \(√( a² - b²) / 4\)
 
 
Perimeter:
 
In here \(a = c\), we have \((P) =\) \(a + b + c\).
 
Substitute the known value.
 
\(P =\) \(a + b + a\) \(=2a+b\)
 
\(P =\) \(2a+b\)
 
Where '\(a\)' is the lengths of the two equal sides and '\(b\)' is 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. That is \(∠ABC\) \(=\) \(∠ACB\).
  • The altitude is a perpendicular distance from the base to the opposite vertex.
Important!
  • When the \(3rd\) angle of an isosceles triangle 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.
  • All the equilateral triangles will satisfy 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(\(A\)) \(=\) \(√3/4 ×s²\) square units.
 
Where '\(s\)' denotes sides of the triangle.
 
 
Perimeter:
 
Perimeter(\(P\)) \(= a + b + c\) or \(P = s + s + s\).
 
Where '\(s\)' is the lengths of the three equal sides.
 
 
Properties:
  • All three angles of an equilateral triangle are the same. Thus, 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 interior angle of an equilateral triangle 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.