Triangles (त्रिभुज) In Hindi
त्रिभुज एक बहुभुज है जिसमें तीन भुजाएँ और तीन शीर्ष होते हैं। यह ज्यामिति की सबसे बुनियादी आकृतियों में से एक है, त्रिभुज के तीनों शीर्षों को A, B और C से दर्शाया जाता है और त्रिभुज को △ABC लिखा जाता है।
त्रिभुज के कुछ महत्वपूर्ण गुण:
त्रिभुज के तीनों कोणों का योग 180 डिग्री होता है।
दो त्रिभुज एक दूसरे के समान हो सकते हैं, अगर उनकी तीनों भुजाएं और तीनों कोण बराबर हैं।
Triangles In English
A triangle is a geometric shape that consists of three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified based on the lengths of their sides and the measures of their angles.
Types
On the basis of length of the sides, triangles are classified into three categories:
1.Scalene Triangle
2.Isosceles Triangle
3.Equilateral Triangle
On the basis of measurement of the angles, triangles are classified into three categories:
1. Acute Angle Triangle
2. Right Angle Triangle
3. Obtuse Angle Triangle
Scalene Triangle: A scalene triangle is a type of triangle, in which all the three sides have different side measures. Due to this, the three angles are also different from each other.
Isosceles Triangle: Two sides are of equal length, and the angles opposite those sides are equal.
Equilateral Triangle: All three sides are of equal length, and all three angles are equal (each measuring 60 degrees).
Acute Triangle: All angles are less than 90 degrees.
Right Triangle: One angle is exactly 90 degrees.
Obtuse Triangle: One angle is greater than 90 degrees.
Properties of Triangle
1. A triangle has three sides, three angles, and three vertices. A vertex is the point where two sides of a triangle meet.
2. The sum of the angles in a triangle is always 180 degrees. This is true for any triangle, regardless of its size or shape. You can prove this by thinking about a triangle as a piece of pie. If you cut a pie into three slices, the slices will always add up to 180 degrees.
3. The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This is known as the Triangle Inequality Theorem. It means that no triangle can have a side that is as long as the other two sides combined.
4. The side opposite the largest angle of a triangle is the longest side. This is also known as the Law of Sines.
5. The side opposite the smallest angle of a triangle is the shortest side.
6. The triangle with the greatest area for a given perimeter is an equilateral triangle. An equilateral triangle is a triangle where all three sides are equal.
Perimeter of Triangle
- Perimeter = Sum of All Sides
Area of a Triangle Formula
- Area of Triangle = \( \frac{1}{2} \) × Base × Height
Heron’s Formula
- A = \( \sqrt{s (s – a) (s – b) (s – c)} \)
Where s is the semi-perimeter of the triangle
- S = \( \frac{(a + b + c)}{2} \)
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