RD Sharma Solutions for Class 9 Maths Chapter 9: Triangle and Its Angles
A Triangle is a figure made up of 3 straight lines (called sides), having 3 vertices (joining at 3 points) and three angles. It is a very basic shape in geometry. The symbol represents a triangle. For example, In△ABC, A, B, and C denote the 3 vertices of the triangle, and the 3 edges will be denoted as AB, BC, CA. The summation of all the angles in a triangle is 180°.
We can distinguish triangles based on two factors, Side & Angle. Based on sides, the triangle can be classified into 3 types:
- A triangle that has at least 2 sides and 2 angles equal in length is called Isosceles Triangle. If one angle is 30°. The other 2 angles will be (180 – 30)/2 = 75°.
- A triangle that has 3 sides equal and 3 equivalent angles is called an Equilateral Triangle. 3 angles in this triangle always measure 60°.
- Triangles having 3 sides different in length along with three different angles is called a Scalene Triangle.
Based on angle, triangles can be classified into 3 types:
- A Right-Angled Triangle is a triangle that has an angle which is 90°. For example, if a right-angled triangle has 2 sides equal, then it is called Right-angled Isosceles Triangle, and the two base angles measure 45° each.
- An Obtuse Triangle is a triangle in which one of the interior angles measure more than 90°.
- A triangle that has all the angles less than 90° is called an Acute-Angled Triangle.
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