11 Plus Triangle
Triangle is a two-dimensional figure which consists of three vertices, three angles and three sides. There are six different types of triangles. In this article, we will study the triangle area, the perimeter of the triangle and the properties of a triangle.
The following figure represents a triangle.
A B and C are vertices of a triangle.
AB, BC and CA are sides of the triangle.
a, b and c are the angles of triangles
Properties of a triangle:
- The sum of the interior angles of a triangle is 180°.
- The sum of the length of any two sides is larger than the third side.
- The difference between any two sides is smaller than the third side.
- The centroid divides the median in a 2:1 ratio.
- An exterior angle is equal to the sum of the opposite two angles.
z= a + b
Types of triangles:
*Triangles are categorized into four types based on the interior angles of a triangle. They are
- Acute angled triangle
- Right-angled triangle
- Obtuse angled triangle
Triangles are categorized into three types based on the length of sides of the triangle. They are
- Scalene triangle
- Isosceles triangle
- Equilateral triangle
Acute angled triangle:
Triangle in which all three angles are less than 90° is called an acute-angled triangle.
a < 90°
b < 90°
c < 90°
A Triangle in which one of the angles is 90° is called a Right-angled triangle.
a = 90°
b + c = 90°
from Pythagoras theorem
Obtuse angled triangle:
A Triangle in which one of the angles is greater than 90° is called an obtuse-angled triangle.
a > 90°
b + c <90°
A Triangle in which the length of all sides are equal, and all angles are equal is called an Equilateral triangle.
AB = BC = CA
A = b = c = 60°
Let assume that AB = BC = CA = a
Triangle in which all sides are different in length and all angles are different is called a Scalene triangle.
AB ≠ BC
BC ≠ CA
CA ≠ AB
a ≠ b
Triangle in which any two sides and two adjacent angles are equal is called the Isosceles triangle.
AC = BC
a = b
The perimeter of a triangle:
The perimeter of the triangle is the sum of the length of three sides.
Perimeter of triangle = AB + BC +CA
Area of a triangle:
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