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 .

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'.

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

If a line through one vertex of a triangle divides the opposite sides in the Ratio of other two sides; then the line bisects the angle at the vertex.

One angle of a triangle is equal to one angle of another triangle and the bisectors of these two equal angles divide the opposite sides in the same ratio, prove that the triangles are similar.

If one angle of a triangle is equal to one angle of another triangle and bisector of these equal angles divide the opposite side in the same ratio; prove that the triangles are similar.