If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
If D E ¯ ∥ B C ¯ , then A D D B = A E E C .
Example :
Find the value of x .
The lines Q R ¯ and S T ¯ are parallel.
Therefore, by the Triangle Proportionality Theorem,
P S Q S = P T R T
Substitute the values and solve for x .
6 2 = 9 x
Cross multiply.
6 x = 18
Divide both sides by 6 .
6 x 6 = 18 6 x = 3
The value of x is 3 .
Answer:
B. Angle Bisector Theorem
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.