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, the height of the triangle \(h = Area × 2 / b\)
And, the base of triangle \(b = Area × 2 / h\)
Where \(h\) is denoted as height.
Where \(b\) is denoted as base.
 
The 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 makes the right angle.
  
Hypotenuse:  The side opposite the right angle is called the hypotenuse. It 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, the height of the triangle \(h = Area × 2 / b\)
And, the base of the triangle \(b = Area × 2 / h\)
Where \(h\) is denoted as height.
Where \(b\) is denoted as base.
Altitude \(h = √( a² - b²) / 4\)
 
The perimeter:
\(P = 2a + b\)
Where \(a\) is the lengths of the two equal sides.
Where \(b\) 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. (\(∠ABC\) 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.
  • All the equilateral triangles will 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.
 
The perimeter:
\(Perimeter (P) = a + b + c\) or \(P = s + s + s\).
\(a\), \(b\), \(c\) are the lengths of the three equal sides.
or
\(s\) is 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.