### Theory:

Right Angle triangle: A triangle where one of its interior angles is a right angle $$90°$$.

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.

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.

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.