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Question

In ΔABC, AD is the median. Which of these conditions should be satisfied to make ΔADB and ΔADC similar triangles?

A
A=90
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B
AB=AC
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C
B=A
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D
BD=AD
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Solution

The correct option is B AB=AC
In the triangles ΔADB and ΔADC,

AD is the common side.

BD = DC (Since D is the midpoint of BC)

For the triangles to be similar, the ratio of corresponding sides of ΔADB and ΔADC should be equal.

ADAD=BDDC=ABAC1=ABACAB=AC

Thus, if AB = AC, then both the triangles can be proved similar.

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