There are four main types of triangles and they are the equilateral triangle, the isosceles triangle, the scalene triangle, and the one we are talking about, the right-angle triangle. A right triangle has a right angle (
) and two acute angles. This property makes it different from the other three triangles.
There are three components of a right-angle triangle and they are hypotenuse, base, and perpendicular (catheti or legs).
Legs or Catheti
The catheti (singular: cathetus) are the sides opposite the acute angles and are the shorter sides of the right triangle.
Base
The base is the side of a triangle where both angles lie. It means that both, acute and right angle lies on the base side.
Hypotenuse
The hypotenuse is the side opposite the right angle and is the largest side of the right triangle.
Area and Perimeter of a Right Triangle
The area of the right-angle triangle is the space entrapped inside of a three-sided triangle. The area of a right triangle is equivalent to half the product of its legs.
The perimeter of the right-angle triangle is the sum of all sides of the triangle. The perimeter of the right-angle triangle tells use the total length of the triangle.
Theorems
1 Pythagorean theorem
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squared base (also known as adjacent) and the squared perpendicular (also known as opposite). Furthermore, this theorem is only valid for the right-angle triangle.
2
In all right triangles, the length one of the legs is a mean proportional between the hypotenuse and the projection on it.
3
In all right triangles, the height of the hypotenuse is a mean proportional between the two segments that it divides.
Examples
The hypotenuse of a right triangle measures 30 cm and the projection of a leg is 10.8 cm on the hypotenuse. Find the length of the other leg.
In a right triangle, the projections of the legs on the hypotenuse are 4 and 9 cm in length. Calculate the height of the triangle.
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I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html