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Question

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

A
A=90
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B
AB=AC
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C
B=C
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D
Either option B or C
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Solution

The correct option is D Either option B or C
In the triangles ΔADB and ΔADC,
AD is the common side and BD = DC (Since D is the midpoint of BC)
Hence ratio of corresponding sides of ΔADB and ΔADC should be equal.
ADAD=BDDC=ABAC1=ABACAB=ACB=C
Hence one of the conditions is enough as the other can be inferred from either Option B or Option C.

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