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### 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 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.

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.

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.