Prove the following statement. "The bisector of an angle of a triangle divides the sides opposite to the angle in the ratio of the remaining sides"

In order to prove, 'The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides. (i) Draw a neat labelled figure. (ii) Write 'Given' and 'To prove'.

Prove:In a triangle the angle bisector divides the side opposite to the angle in the ratio of the remaining sides.

Atempt any two of the following : Prove : In a triangle the angle bisector divides the side opposite to the angle in the ratio of the remaining sides.

The external angle bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

The external angle bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

The internal angle bisector of an angle of a triangle divide the opposite side internally in the ratio of the sides containgthe angle

Read the statemenst carefully and state 'T' for true and 'F' for false . 1. If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle . 2 . The internal bisector of an angle of a triangle divides the opposite side inernally in the ratio of the sides containing the angle . 3 . If a line through one vertex of a triangle divides the opposite in the ratio of other two sides , then the line bisects the angle at the vertex . 4.Any line parallel to the parallel sides dividesproportionally . 5. Two times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle .

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

If the bisector of an angle of a triangle bisects the opposite side,prove that the triangle is isosceles.