What is Angle Bisector Theorem?
Answers
Answer:
In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
Answer:
The angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
Given : A ΔABC in which AD is the internal bisector of ∠A and meets BC in D.
Prove that : BD / DC = AB / AC
Construction : Draw CE || DA to meet BA produced in E.
Statements Reasons
1) CE || DA 1) By construction
2) ∠2 = ∠3 2) Alternate interior angles
3) ∠1 = ∠4 3) Corresponding angles
4) AD is the bisector 4) Given
5) ∠1 =∠2 5) Definition of angle bisector
6) ∠3= ∠4 6) From (2) and (3)
7) AE = AC 7) In ΔACE, side opposite to equal angles are equal