### Triangle

A triangle is a closed curve made of three line segments. It has three vertices, three sides and three angles. Here in ΔABC, it has

Classification of triangles based on sides

- A triangle having three unequal sides is called a scalene triangle.
- A triangle having two equal sides is called an isosceles triangle.
- A triangle having three equal sides is called an equilateral triangle.

Classification of triangles based on angles

- If each angle is less than 90°, then the triangle is called an acute-angled triangle.
- If anyone angle is a right triangle, then the triangle is called a right-angled triangle.
- If anyone angle is greater than 90°, then the triangle is called an obtuse-angled triangle.

**Medians of a Triangle**

The line-segment joining a vertex of a triangle to the mid-point of its opposite side is called a median of the triangle. Since there are three vertices in a triangle, therefore, a triangle has three medians.

**Altitudes of a Triangle**

A line segment drawn from a vertex of a triangle perpendicular to its opposite side is called an altitude (height) of the triangle corresponding to the opposite side. Since there are three vertices in a triangle, therefore, a triangle has three altitudes.

**Exterior Angle of a Triangle and its Property**

An exterior angle of a triangle is formed when a side of a triangle is produced. At each vertex, we have two ways of forming an exterior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.

**Angle Sum Property of a Triangle**

The sum of the measures of the three angles of a triangle is 180°.

### Pythagoras Theorem

- The side opposite to the right angle in a right-angled triangle is called the hypotenuse.
- The other two sides are known as legs of the right-angled triangle.
- In a right-angled triangle, square of hypotenuse is equal to the sum of squares of legs.

AC^{2}=AB^{2}+BC^{2}

⇒5^{2}=4^{2}+3^{2}

NCERT Solutions