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Question

In \(\Delta{ABC}\), AB = AC and AD is the median. Then by which similarity are the \(\Delta{ADB}\) and \(\Delta{ADC}\) similar?

A
SSS
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B
SAS
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C
Both a and b
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D
None of these
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Solution

The correct option is C Both a and b
In the triangles ΔADB and ΔADC,
AD is the common side
BD = DC [Since D is the midpoint of BC]
and AB = AC [Given]
So, ratio of corresponding sides is ADAD=BDDC=ABAC=1
Therefore the triangles are similar by SSS similarity.
But SSS is not in the given option
So,
In the triangles ΔADB and ΔADC,
AB = AC [Given]
B=C
[Since AB = AC, angles opposite to equal sides are equal]
BD = DC [Since D is the midpoint of BC]
Therefore the triangles are similar by SAS similarity.

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