The triangle is a closeup of the door polygon that has three angles, 3 sides, and three vertices. Based top top the length of sides and also measure of angles, the triangles room classified into different varieties of triangles.Properties the a triangle assist us to recognize a triangle from a given collection of figures easily and also quickly.

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In the beginning, we begin from expertise the form of triangles, your types, and also properties, theorems based on them such together Pythagoras theorem, etc. Let united state learn right here some basic properties of triangles.

1.Triangles: group by Type
2.Triangle Properties
3.Solved Examples
4.Practice Questions
5.FAQs

Triangles: group by Type


Triangles have the right to be classified right into two broad categories based upon their angles and sides. Based upon angles, there space 3 types of triangles, and based on sides, there space 3 types of triangles.

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Triangle Properties


Properties of a triangle aid us to recognize relationships between different sides and also angles the a triangle. Few of the necessary properties the a triangle are provided below.

Property 1 - Angle sum Property

As every the angle sum property, the sum of the three inner angles that a triangle is always 180°.

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In the provided triangle, angle ns + edge Q + angle R = 180°

Property 2 - Triangle Inequality Property

As per the triangle inequality property, the amount of the length of the 2 sides the a triangle is better than the third side.

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In △ ABC and △ PQRa + b > c ( 6 + 4 > 3)c + a > b (3 + 4 > 6)c+ b > a ( 6 + 3 > 4)

Property 3 - Pythagorean Theorem

As per the Pythagorean theorem, in a best triangle, the square the the hypotenuse equates to the amount of the squares that the various other two sides. Mathematically, it have the right to be expressed together Hypotenuse² = Base² + Altitude².

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Property 4 - side opposite the better angle is the longest side

In order to recognize the next opposite the higher angle is the longest side property, let's take it the below-given triangle into consideration.

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In this triangle, edge B is the biggest angle. Thus, the next AC is the longest side.

Property 5 - Exterior angle Property

As every the exterior angle property, the exterior angle of a triangle is always equal come the amount of the internal opposite angles.

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In the provided triangle, Exterior angle E1 = edge PQR + edge QRPThere space 3 exterior angles in a triangle and also all these exterior angles include up come 360° for any type of polygon.

Property 6 - Congruence Property

As every the Congruence Property, two triangles are claimed to it is in congruent if every their corresponding sides and also angles are equal.

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angle XYZ = edge DEFangle YXZ = edge EDFangle YZX = angle EFDXY = DEXZ = DFYZ = EF

The an easy triangle nature such together the area and also perimeter that a triangle are given below.

Area the a triangle: The complete amount of an are inside the triangle is called the area that a triangle. The area is measure up in square units.The general formula for calculating the area the a triangle is Area (A) = (1/2) × base × HeightPerimeter: The perimeter the a triangle = amount of all its 3 sides

Heron's formula: Heron’s formula is supplied to calculate the area the a triangle if the lengths of all the sides room known and the height of the triangle is not known. First, we have to calculate the semi-perimeter(s). For a triangle v sides p, q, and also r, s = (p+q+r)/2, the area is given by; A = \(\sqrtS(S-P)(S-Q)(S-R)\)

Properties the a Triangle connected Topics

Check the end these interesting short articles to know much more about properties of a triangle and its related topics.

Important Notes

The triangle is a closed polygon that has actually three angles, three sides, and three vertices.Sides and angles are an extremely important facets of a triangle.We deserve to classify various types of triangles in mathematics by combine sides and angles.The basic formula because that calculating the area of a triangle is Area (A) = (1/2) × base × HeightThe perimeter the a triangle is same to the sum of all three sides the the triangle.

Example 3:A triangle has a dimension of 3 cm, 4 cm, and also 5 cm, where the base is 4 cm and the altitude of the triangle is 3.2 cm. Calculatethe area and also perimeter that the triangle.

Solution:

Sides the the triangleare: x= 3 cm, y= 4 cm and also z= 5 cmAltitude= 3.2 cm

Using the area of the triangle formula, us know, Area = 1/2 × basic × heightA = (1/2) × 4 × 3.2A = 6.4 sq.cm.

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The perimeter the the triangle is given by p = x+ y+ zP = 3 + 4 + 5P = 12 cmTherefore, the area and also perimeter that the given triangle are 6.4 cm2 and 12 centimeter respectively.