Question

In $\Delta ABC$, AD is the median. Which of these conditions should be satisfied to make $\Delta ADB$ and $\Delta ADC$ similar triangles?

• A. $\angle A={90}^{\circ }$
• B. $AB=AC$
• C. $\angle B=\angle A$
• D. $BD=AD$

Answer 1

The correct option is B $AB=AC$

In the triangles $\Delta ADB$ and $\Delta ADC$,

AD is the common side.

BD = DC (Since D is the midpoint of BC)

For the triangles to be similar, the ratio of corresponding sides of $\Delta ADB$ and $\Delta ADC$ should be equal.

$\Rightarrow \frac{AD}{AD}=\frac{BD}{DC}=\frac{AB}{AC}\Rightarrow 1=\frac{AB}{AC}\Rightarrow AB=AC$

Thus, if AB = AC, then both the triangles can be proved similar.