Question

In $\Delta ABC$, AB = AC and AD is the median. $\Delta ADB$ and $\Delta ADC$ are

• A. similar by AA similarity criterion
• B. similar by SAS similarity criterion
• C. similar by SSS similarity criterion
• D. not similar

Answer 1

The correct option is C similar by SSS similarity criterion

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

AB = AC (given)

AD is common in both the triangles.

Since AD is the median, BD = CD.

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

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

Also, $△ADB$ and $△ADC$ are congruent as all the corresponding sides are equal.