Question

In the given figure, OA=OB and OD=OC then which of the following is true? ​

Answer 1

Given :- In the given figure, OA=OB and OD=OC then which of the following is true ? 

A) ∆BOC ~ ∆AOD

B) ∆BOC ~ ∆DOA

C) ∆OBC ~ ∆AOD

D) ∆BOC ~ ∆ADO

Solution :

in ∆BOC and ∆AOD we have ,

→ OB = OA (given)

→ ∠BOC = ∠AOD (given)

→ OC = OD (given).

Therefore,

→ ∆BOC ~ ∆AOD (By SAS similarity).

Hence Option A is true.

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3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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Answer 2

Given OA×OB=OC×OD

Then We have

 OCOA=OBOD....(1)

In ΔAOD and ΔCOB 

OCOA=OBOD....from (1)

∠AOD=∠COB[verticallyopp.∡S]

∴ΔAOD∼ΔCOB( SAS)

Now, if two triangle are similar. so, corresponding angles are equal.

∠A=∠C

and ∠D=∠B