Question

In the figure l ∥m, ∠AOD =90

and ∠ODB =30

. Are △OCA and △ODB

similar? If yes, by which criterion?​

Answer 1

Angle AOC = Angle DOB (Vertically Opposite angles)

Angle OBD = Angle CAO (explained above)

Therefore OCA~ODB By AA criteria

Answer 2

Given :   l ∥m ∠AOD =90 °  and ∠ODB =30°

To Find :   Are △OCA and △ODB Similar

Solution:

We even Does not need ∠AOD  value

As ∠AOC = ∠BOD  ( vertically opposite angle )

As ∠AOD   = 90 °

Hence ∠AOC = ∠BOD  = 90°

∠OCA = ∠ODB    ( interior  alternate angles )

∠OAC = ∠OBD    ( interior  alternate angles )

in  △OCA and △ODB

∠AOC = ∠BOD  

∠OCA = ∠ODB  

∠OAC = ∠OBD  

Triangles are Similar using AA or AAA criteria

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