In the figure, \( AB = 3 \) cm, \( AC = 6 \) cm, \( BD = 2 \) cm and \( CD = 4 \) cm. The ratio of \( \angle BAD \) and \( \angle CAD \) will be:
Show Hint
The Angle Bisector Theorem states that the angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.
In triangle \( \triangle ABC \), the point \( D \) lies on side \( BC \).
Since \( AD \) is the angle bisector of \( \angle BAC \), by the Angle Bisector Theorem, the angle bisector divides the opposite side into segments that are proportional to the adjacent sides. This means:
\[
\frac{BD}{DC} = \frac{AB}{AC}
\]
Substitute the given values:
\[
\frac{2}{4} = \frac{3}{6}
\]
Simplifying both sides:
\[
\frac{1}{2} = \frac{1}{2}
\]
Thus, the ratio of the two angles \( \angle BAD \) and \( \angle CAD \) is \( 1 : 1 \).
Step 2: Conclusion.
Therefore, the ratio of \( \angle BAD \) to \( \angle CAD \) is \( 1 : 1 \).
