Question

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

• A. $\angle A={90}^{\circ }$
• B. $AB=AC$
• C. $\angle B=\angle C$
• D. $\text{Either option B or C}$

Answer 1

The correct option is D $\text{Either option B or C}$

In the triangles $\Delta$ADB and $\Delta$ADC,
AD is the common side and BD = DC (Since D is the midpoint of BC)
Hence ratio of corresponding sides of $\Delta$ADB and $\Delta$ADC should be equal.
$\frac{AD}{AD}=\frac{BD}{DC}=\frac{AB}{AC}\Rightarrow 1=\frac{AB}{AC}\Rightarrow AB=AC\Rightarrow \angle B=\angle C$
Hence one of the conditions is enough as the other can be inferred from either Option B or Option C.