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# Triangle: Vital shape of Geometry

On a daily basis, various shapes are used. Shapes have always been an important part of one’s life. In our daily lives, we encounter a wide range of shapes. Shapes have been used in mathematics because they are related. There are numerous shapes that we encounter on a daily basis, such as squares, rectangles, or circles, and let us not forget the most important shape that we encounter, the triangle. The use of a triangle entails much more than simply determining its perimeter or area.

Geometry is a branch of mathematics that is an infinite field. It is simply impossible to believe that geometry is used on a daily basis. Geometry is the study of shapes and sizes, as well as position and angles. It not only deals with two-dimensional shapes such as a square, triangle, or rectangle, but also with three-dimensional shapes such as cubes, cuboids, and many others. It is one of mathematics’s oldest

branches. It is classified into three types: Euclidean, spherical, and hyperbolic. Geometry and shapes go hand in hand. For the time being, let’s talk about the shape triangle.

Let’s talk about what the triangle is all about. It is a shape with three sides, and the sum of all the angles on those sides is approximately 180 degrees.

•  A triangle’s size is determined by its three sides, and its shape is determined by its three angles. .
•  They are the same size and shape. Triangles have numerous congruence conditions.The triangle congruence theorem for triangle congruence criteria aid in determining whether or not a triangle is congruent.
•  Congruent triangles means exactly the same in shape and size no matter how we turn, flip, or rotate it. Congruent figures are shapes that can be superimposed on

each other in geometry; for example, triangles and quadrilaterals can be congruent.

The triangle congruence theorems or triangle congruence criteria listed below aid in proving triangle congruence.

• S.S.S (Side, Side, Side)
• S.A.S. (Side, Angle, Side)
• A.S.A. (Angle, Side, Angle)
• A.A.S (Angle, Angle, Side)

The RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)

• According to the Side-Side-Side theorem, if two triangles are considered to be congruent then they have all the sides equal in length.
• Side-Angle-Angle (ASA) According to the theorem, if two triangles are considered congruent, the two corresponding angles equal to each other will have a corresponding side equal to each other.
• According to the Side-Angle-Side (SAS) congruence theorem, if two corresponding sides of two triangles are equal,including the corresponding angles formed by these sides, the two triangles are congruent.
• According to the Angle-Angle-Side congruence theorem, if two angles of a triangle with a side not included between the angles are equal to the corresponding angles and side of the other triangle.
• Similar triangles are those with corresponding sides that are proportional to each other and corresponding angles that are equal to each other.
• Similar triangles appear to be the same, but their sizes can vary. Similar triangles differ from congruent triangles in general.
• Similar triangles are triangles that have a similar appearance but may not be exactly the same size.
• Two objects are said to be similar if they have the same shape but differ in size.

That is, when similar shapes are magnified or demagnified, they superimpose on each other. This property of similar shapes is known as “Similarity.”

This was only a brief discussion of triangles. To learn more about triangles, conduct a Google search for cuemath to clear up any confusion about the subject. Many students’ weak concepts have been cleared with the help of cuemath.

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