### 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, 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.

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.

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.