More about Triangles

More about Triangles

Points to be Remember:-

1. If two sides of a triangle are equal, then their opposite angles are

     also equal.

2. If two angles of a triangle are equal, then their opposite sides are

    also equal.

Points to be Remember:-

1. Pythagoras theorem: In a right angled triangle, the square of

    hypotenuse equals the sum of the square of its side

2. In a right angled triangle, the hypotenuse is the longest side.

3. If the square of one side of a triangle is equal to the sum of the

    squares of the remaining two sides, then the angle opposite the

    first side is a right angle.

Points to be Remember:-

1. The perpendicular line segment drawn from any vertex of a triangle 

     into the opposite side is called altitude of the triangle.

2. A triangle has three altitudes. From each vertex one altitude is

    Obtained

3. The altitudes of a triangle are concurrent. The point of

     concurrence of the altitudes of a triangle is called the orthocenter

     of the triangle.

4. The line segment joining any vertex of a triangle to the mid-point of

     its opposite side is known as median of the triangle.

5. A triangle has three vertices and from each vertex one median is

     obtained. Thus a triangle has three medians.

6. The medians of a triangle are concurrent. The point of concurrence

     of the medians of a triangle is called centroid of triangle.

Points to be Remember:-

1. A perpendicular bisector of a side of a triangle is the line that is

    perpendicular to the side and bisects it.

2. A triangle has three sides. Therefore, it has three perpendicular

    bisects.

3. The perpendicular bisects of the sides of a triangle are concurrent.

    The point of concurrence of the perpendicular bisectors of the 

    sides of a triangle is called the circumcentre of the triangle.

4. An angle bisector of a triangle is the line segment which bisects a

     angle of the triangle and has its other end point on the opposite

     side of that angle.

5. A triangle has three angles and each angle has a bisector.

     Therefore a triangle has three angle bisector.

6. The angle bisector of a triangle are concurrent. The point of

     concurrence of the angle bisectors of a triangle is called its

     incentre.