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Published by Programme B
Geometry has always been one of the most fundamental disciplines taught in schools. “The study of shapes and their interactions with one other and with the space surrounding them” is how geometry is defined. Geometry examines length, angle, area, among several other things. In this article, we will be seeing the kinds of triangles, be it the area of right triangle or equilateral triangle.
Geometry begins with the smallest shape, a dot, and progresses to lines, intersections, and the development of figures through the junction or positioning of these lines at various angles and lengths. As a result, a large number of figures are generated.
Triangle is the first closed shape that geometry has, which is made up of three straight lines. The lines form the angles on the inside whose sum is equal to 180 degrees. Thus, a triangle has three internal angles. Also, a triangle has three line segments, and they can be of varying lengths. Hence, depending upon the angles that the lines make and also their individual measures, the triangles can be classified into many types, such as isosceles triangle, scalene triangle, equilateral triangle, or right-angled triangle. Also, based on the angles, they may also be classified as the acute-angled triangle, obtuse-angled triangle, right-angled triangle, and so on.
In geometry, one of the most major concept is of the measurements as measurements of figures help us understand how much space they are taking up in space, and this concept has its utility in the whole wide world in engineering, architecture, etc.
If we talk of a right-angled triangle, since the two sides of a right-angled triangle are perpendicular to each other, the base and height are plainly visible. Trigonometry is supported by the concept of right-angled triangles. The two lengths and the hypotenuse are the three values of a right-angled triangle and form the basis of the Pythagoras theorem also. The area of the right-angled triangle would be ½ × base × height, and the area will be in square units.
Similarly, if we talk of the area of equilateral triangle, then since each of the internal angles of an equilateral triangle is sixty degrees, and all of the sides are the same length. Its area is calculated by this formula which is equal to [(Square root of 3) × a 2] /4.
Different triangles have different properties, too, like if we talk of right-angled triangles, the hypotenuse of the triangle is the longest side, and it is the side opposite the right angle.
The Cathetus refers to the triangle’s sides that are situated adjacent to the right angle. The right-angled triangle’s three major dimensions or values are the two lengths and the hypotenuse. If any one of the side measurements is missing, with the help of the Pythagoras theorem, the third can be found out easily. Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the individual squares of base and height.
The perimeter of a right-angled triangle is equal to the measure of the sum of its three sides. The concept of right-angled triangles underpins trigonometry. To know more about trigonometry and to work more on triangle problems, students are advised to practice geometry worksheets which can be downloaded from the Cuemath website. Cuemath features dynamic and logically designed worksheets that help students improve their analytical skills while also giving them a thorough understanding of geometry topics. Understanding the many sorts of geometrical shapes and how to calculate them is crucial for further math studies.
Photo by Sam Lion from Pexels