Question
If line segment AD is an angle bisector and AB=6, AC = 10, and BD = 3, what must DC equal?
- 8
- 9
- 10
- 5
Hint:
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.
The correct answer is: 8
Angle bisector theorem
Hence, the correct option is A.
Here, the value of DC is 5.
Related Questions to study
Choose the correct statement for the angle bisector theorem to the following triangle.
The base is divided in the same ratio as the sides containing the angle.
Choose the correct statement for the angle bisector theorem to the following triangle.
The base is divided in the same ratio as the sides containing the angle.
Theorem used to find the value of AB in the following figure
Here, AB = 4√2.
Theorem used to find the value of AB in the following figure
Here, AB = 4√2.
To find the value of AB in the figure, which theorem is used?
If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.
To find the value of AB in the figure, which theorem is used?
If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.
Which of the statements is true in the case of the given triangle?
The base is divided in the same ratio as the sides containing the angle.
Which of the statements is true in the case of the given triangle?
The base is divided in the same ratio as the sides containing the angle.
To find the value of p, which statements can be used?
Her, the value of p is 43.5.
To find the value of p, which statements can be used?
Her, the value of p is 43.5.
In the figure, to find the value of x which theorem can be used?
Here, the value of x is 10.
In the figure, to find the value of x which theorem can be used?
Here, the value of x is 10.
It is also called basic proportionality theorem.
It is also called basic proportionality theorem.
Find the length of the segment AB
It is also called basic proportionality theorem or Thales' theorem.
Find the length of the segment AB
It is also called basic proportionality theorem or Thales' theorem.
In the given triangle 
then the line segment DE ll AC
It is also called midpoint theorem.
In the given triangle then the line segment DE ll AC
It is also called midpoint theorem.
