If the line through one vertex of the triangle internally divides the opposite side such that they are proportional to the sides containing the angle, then the line must bisect the vertex angle.

True

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False

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Solution

The correct option is A
True

The converse of angle bisector theorem states that if the line through one vertex of the triangle internally divides the opposite side such that they are proportional to the sides containing the angle, then the line must bisect the vertex angle.

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Similar questions

Q. In any triangle, a line from a vertex to its opposite side, bisecting the interior angle at that vertex is called -

If a line through ∠B divides the opposite side in proportion to the sides containing ∠B, then p : q = .

Assertion (A): If one angle of a triangle is equal to one angle of another triangle and bisectors of these angles divide the opposite sides in the same ratio, then the triangles are similar.
Reason (R): The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

Which of the following is true?

Q. Prove that the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

Q. Line segment joining the vertex with the midpoint of the opposite side of the triangle is called angle bisector.

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If the line through one vertex of the triangle internally divides the opposite side such that they are proportional to the sides containing the angle, then the line must bisect the vertex angle.

The correct option is A True The converse of angle bisector theorem states that if the line through one vertex of the triangle internally divides the opposite side such that they are proportional to the sides containing the angle, then the line must bisect the vertex angle.

The correct option is A
True

The converse of angle bisector theorem states that if the line through one vertex of the triangle internally divides the opposite side such that they are proportional to the sides containing the angle, then the line must bisect the vertex angle.