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Question

In ΔABC, AB = AC and AD is the median. ΔADB and ΔADC are 



  1. similar by AA similarity criterion
  2. similar by SAS similarity criterion
  3. similar by SSS similarity criterion
  4. not similar


Solution

The correct option is C similar by SSS similarity criterion
In ΔADB and ΔADC,

AB = AC (given)

AD is common in both the triangles.

Since AD is the median, BD = CD.

ABAC=ADAD=BDCD=1

ADBADC (by SSS similarity criterion)

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

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