Question

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

• A. SSS
• B. AA
• C. SAS
• D. None of the above

Answer 1

The correct option is A SSS

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

AD is the common side

BD = DC (Given, AD is the median so, D is the midpoint of BC)

AB = AC (given)

So, ratio of corresponding sides is

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

$\therefore △ADB\sim △ADC$
(by SSS similarity criterion)