In - ABC - AD is the median and AB - AC- Then by which similarity criterion are - ADB and - ADC similar-A- SASB- SSSC- AAD- None of the above

The correct option is B SSSIn ΔADB and ΔADC, AD is the common side BD = DC nbsp; nbsp;(Given, AD is the median so, nbsp;D is the midpoint of BC) AB = ...

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Standard X

Mathematics

SSS Similarity

In Δ ABC , AD...

Question

In $Δ$ ABC, AD is the median and AB = AC. Then by which similarity criterion are $Δ$ ADB and $Δ$ ADC similar?

SSS

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SAS

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None of the above

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Solution

The correct option is A SSS
In $Δ$ ADB and $Δ$ ADC,

AD is the common side

BD = DC (Given, AD is the median so, D is the midpoint of BC)

AB = AC (given)

So, ratio of corresponding sides is

$\frac{A D}{A D} = \frac{B D}{D C} = \frac{A B}{A C} = 1$

$∴ △ A D B \sim △ A D C$
(by SSS similarity criterion)

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In Δ ABC, AD is the median and AB = AC. Then by which similarity criterion are Δ ADB and Δ ADC similar?

The correct option is A SSSIn ΔADB and ΔADC, AD is the common side BD = DC (Given, AD is the median so, D is the midpoint of BC) AB = AC (given) So, ratio of corresponding sides is ADAD=BDDC=ABAC=1 ∴△ADB∼△ADC (by SSS similarity criterion)

In $Δ$ ABC, AD is the median and AB = AC. Then by which similarity criterion are $Δ$ ADB and $Δ$ ADC similar?