Question

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

• A. SSS
• B. SAS
• C. Both a and b
• D. None of these

Answer 1

The correct option is C Both a and b

In the triangles $\Delta$ADB and $\Delta$ADC,
AD is the common side
BD = DC [Since D is the midpoint of BC]
and 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.