Triangle class 9

A triangle is a closed shape  with three sides, three vertices, and three angles. ABC is the symbol for a triangle having three vertices, A ,B and C. 180 degrees is the total of all three angles and  Any triangle’s total exterior angles are equal to 360°.Signboards and sandwiches in the shape of a triangle are two of the most common instances of triangles.

Triangle:-

A triangle is a 3 sided polygon with 3 inner angles. It is one of the most fundamental shapes in geometry, consisting of 3 vertices linked together and symbolised by the symbol ‘△’. The sides and angles of a triangle are used to classify it into several sorts.

When we talk about parts of a triangle, it is made up of several pieces. It has  3 angles,  3 sides, and 3  vertices.

Properties of triangle:-

All geometrical shapes have different side and angle features that help us identify them.  A list of the most important qualities of a triangle are given below:-

• Angle sum property of the triangle is the sum of a triangle’s interior angles is always 180 degrees. The angle sum property of a triangle is the name for this property.

• The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, according to Pythagoras’ theorem. i.e. (h²= p²+b²).

• Three sides, three vertices, and three internal angles comprise a triangle.

• According to the Triangle Inequality Theorem, the length of the two sides of a triangle is higher than the length of the third side.

• The opposing side of the larger angle has the longest side.

• The exterior angle of a triangle is always equal to the sum of the interior opposite angles, according to the triangle’s exterior angle theorem.

Triangle’s formula :-

Every two-dimensional shape has two basic measurements that must be determined in geometry, namely the area and perimeter of that shape called triangle . As a result, there are two basic formulas for calculating the area and perimeter of a triangle.

• perimeter of triangle:-

        The  perimeter of the triangle is equal to the sum of its three bounded sides.

         Let us suppose a triangle ABC . Sides of the triangle are AB, BC and AC.

        So,the perimeter of the triangle is the sum of these given sides of the triangle .

        i.e. perimeter of triangle = AB +BC+ AC.

• Area of triangle

The area of a triangle means how much space a figure covers. It is equal to half of the sum of its base and altitude (height). Because it is two-dimensional, it is always measured in square units. 

         i.e. area of triangle= 12× base×height .

Classification of triangle:-

The sides and angles of a triangle can be used to classify triangles.

To classify triangles based on their angles, we measure each of their inner angles, and the triangles can then be classed as follows:

• An acute triangle is one in which all of the inner angles are acute (less than 90 degrees).
• Triangle with a Right Angle: A right triangle has one right angle (90°).
• A triangle with one obtuse angle (more than 90°) is called an obtuse triangle.

We measure the length of each side of the triangle for classification, and triangles can be classed by their sides as follows:

• Equilateral Triangle: An equilateral triangle is a type of triangle in which all the three sides are of the same length. All three angles will be equal because all three sides are the same length. An equilateral triangle’s interior angles are all 60 degrees.

• Isosceles Triangle: An isosceles triangle is a triangle with two sides of equal length and a third side of a different length.

   The angles on the opposing  sides of the equal sides are the same.

• Scalene Triangle: A scalene triangle is a triangle with three sides of varying lengths.

Because the three sides have various lengths, the three angles will be different sizes as well.

Similar triangle:-

Similar triangles are triangles that have a similar appearance but differ in size. When two objects have the same shape but differ in size, they are considered to be comparable. That is, when similar shapes are amplified or demagnified, they superimpose. “Similarity” refers to the property of comparable shapes.

Rules of Similarity

• AAA Angle-Angle-Angle)
• SAS (Side-Angle-Side)
• SSS (Side-Side-Side)
• RHS (Right Angle- Hypotenuse-Side)

Triangle’s congruence :-

When a triangle’s three angles and three sides are the same as the corresponding angles and sides of another triangle, the two triangles are said to be congruent.

Conditions for congruence:-

Two triangles are said to be congruent if their size and shape are the same. To prove that both triangles are congruent, you don’t have to find all six corresponding elements. According to studies and trials, there are five requirements for two triangles to be congruent. SSS, SAS, ASA, AAS, and RHS are the congruence properties.

Conclusion:-

A closed shape having 3 sides, 3 vertices, and 3 angles is known as triangle . ABC is the symbol for a triangle having three vertices, A ,B and C. 180 degrees is the total of all three angles and  Any triangle’s total exterior angles are equal to 360°.There are various properties of triangles .The sides and the angles of the triangle can be used to categorise it.