Question

In $\Delta ABC$, AB = AC and AD is the median. Then by which similarity are the $\Delta ADB$ and $\Delta ADC$ similar?

Answer 1

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

• AD is the common side
• BD = DC [Since D is the midpoint of BC]
• AB = AC [Given]

So, ratio of corresponding sides is $\frac{AD}{AD}=\frac{BD}{DC}=\frac{AB}{AC}=1$

Therefore the triangles are similar by SSS similarity.

But SSS is not in the given option
So, In the triangles $\Delta$ADB and $\Delta$ADC:

• AB = AC [Given]
• $\angle B=\angle C$ [Since AB = AC, angles opposite to equal sides are equal]
• BD = DC [Since D is the midpoint of BC]

Therefore the triangles are similar by SAS similarity.