Question

Choose the correct ratio for the angle bisector theorem for this triangle.

• A. $\frac{AB}{AC}=\frac{AD}{AC}$
• B. $\frac{BD}{DC}=\frac{AB}{AC}$
• C. $\frac{DC}{AC}=\frac{AD}{BD}$
• D. $\frac{AB}{AD}=\frac{BC}{BD}$

Answer 1

The correct option is B $\frac{BD}{DC}=\frac{AB}{AC}$

Consider $\Delta ABC$.Let the angle bisector of angle A intersect side BC at a point D between B and C. The angle bisector theorem states that the ratio of length of the line segment BD to the length of segment DC is equal to the ratio of the length of side AB to the length of side AC:

$\frac{BD}{DC}=\frac{AB}{AC}$