Notes On Triangles - CBSE Class 7 Maths

A triangle is a closed figure made of three line segments. Every triangle has three sides, three angles, and three vertices. These are known as the parts of a triangle.

Classification of triangles
The types of triangles classified by their sides are:

  • Equilateral triangle
  • Isosceles triangle
  • Scalene triangle

The types of triangles classified by their angles are:

  • Right angled triangle
  • Obtuse angled triangle
  • Acute angled triangle

Equilateral triangle:
A triangle in which all the sides are equal is called an equilateral triangle. All the three angles of an equilateral triangle are also equal, and each measures 60°.

Isosceles triangle:
A triangle in which any two sides are equal is called an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are called the base angles, and they are equal.

Scalene triangle:
A triangle in which no two sides are equal is called a Scalene triangle.

Acute-angled triangle:
A triangle with all its angles less than 90° is known as an acute-angled triangle.

Obtuse-angled triangle:
A triangle with one of its angles more than 90° and less than 180° is known as an obtuse-angled triangle.

Right-angled triangle:
A triangle with one of its angles equal to 90° is known as a right-angled triangle. The side opposite the vertex with 90° angle is called the hypotenuse, and is the longest side of the triangle.

Median
The line segment drawn from a vertex of a triangle to the midpoint of the opposite side is called a median of the triangle. Three medians can be drawn from each vertex of a triangle. Medians of a triangle are concurrent. The point of concurrence is called the centroid of the traingle, and is denoted by G.

The centroid and medians of a triangle always lie inside the triangle. The centroid of a triangle divides the median in the ratio 2:1.

Altitude
The line segment drawn from the vertex of a triangle which is perpendicular to the opposite side of that triangle is called an altitude of the triangle. A triangle has three altitudes. The altitudes of a triangle are concurrent. The point of concurrence is called the orthocentre, and is denoted by O.

The altitude and orthocentre of a triangle need not lie inside the triangle.

Summary

A triangle is a closed figure made of three line segments. Every triangle has three sides, three angles, and three vertices. These are known as the parts of a triangle.

Classification of triangles
The types of triangles classified by their sides are:

  • Equilateral triangle
  • Isosceles triangle
  • Scalene triangle

The types of triangles classified by their angles are:

  • Right angled triangle
  • Obtuse angled triangle
  • Acute angled triangle

Equilateral triangle:
A triangle in which all the sides are equal is called an equilateral triangle. All the three angles of an equilateral triangle are also equal, and each measures 60°.

Isosceles triangle:
A triangle in which any two sides are equal is called an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are called the base angles, and they are equal.

Scalene triangle:
A triangle in which no two sides are equal is called a Scalene triangle.

Acute-angled triangle:
A triangle with all its angles less than 90° is known as an acute-angled triangle.

Obtuse-angled triangle:
A triangle with one of its angles more than 90° and less than 180° is known as an obtuse-angled triangle.

Right-angled triangle:
A triangle with one of its angles equal to 90° is known as a right-angled triangle. The side opposite the vertex with 90° angle is called the hypotenuse, and is the longest side of the triangle.

Median
The line segment drawn from a vertex of a triangle to the midpoint of the opposite side is called a median of the triangle. Three medians can be drawn from each vertex of a triangle. Medians of a triangle are concurrent. The point of concurrence is called the centroid of the traingle, and is denoted by G.

The centroid and medians of a triangle always lie inside the triangle. The centroid of a triangle divides the median in the ratio 2:1.

Altitude
The line segment drawn from the vertex of a triangle which is perpendicular to the opposite side of that triangle is called an altitude of the triangle. A triangle has three altitudes. The altitudes of a triangle are concurrent. The point of concurrence is called the orthocentre, and is denoted by O.

The altitude and orthocentre of a triangle need not lie inside the triangle.

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