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**. The sides and the angles of every triangle differ from one another; therefore, they do not look alike.- Based on their sides, there are
**equilateral**,**isosceles**and**scalene****triangles**. - Based on their angles, there are
**acute**,**obtuse**and**right-angled****triangles**.

**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 an 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 90° angle**is called the**hypotenuse,**and is the**longest side of the triangle**.
Mark the

**mid-point**of the side of a triangle, and join it to its opposite vertex. This**line****segment**is called a**median**. It is defined as a line segment drawn from a**vertex**to the**mid-point**of the opposite side. You can draw three**medians**to a given triangle. The medians pass through a common point. Hence, the medians of a triangle are**concurrent**. This**point of concurrence**is called the**centroid,**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

**altitude of a triangle**is a**line****segment**drawn from a**vertex**and is**perpendicular**to the opposite side. 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.**Properties of Triangles**

- An exterior angle of a triangle is equal to the sum of its interior opposite angles.
- The total measure of the three angles of a triangle is 180°.
- Sum of the length of any two sides of a triangle is greater than the length of the third side.
- In a right-angled triangle, the side opposite to the right angle is called the hypotenuse and the other two sides are called its legs.
- The Pythagoras Property states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the legs.
- If the Pythagoras Property holds, the triangle must be right-angled.

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