Теория:

Right Angle triangle: A triangle where one of its interior angles is a right angle \(90°\).
 
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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.
 
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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".
Important!
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.
 
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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.