Question

In the given figure, AB and CD intersect at O. If AC = DB and $\angle ACO=\angle DBO$ then which of the following is true ?

• A. $△AOC\cong △DOB$ by AAS postulate
• B. $△AOC\cong △DOB$ by SAA postulate
• C. AO = DO
• D. O is midpoint of CD

Answer 1

Answer: (A), (C)

The correct options are
A

$△AOC\cong △DOB$ by AAS postulate

C

AO = DO

In $△AOC$ and $△DOB$

(i) $\angle AOC=\angle DOB$ .........(vertically opposite angles)

(ii) $\angle ACO=\angle DBO$ .......(given)

(iii) AC = DB .......(given)

(iv)$△AOC\cong △DOB$ .......(AAS Postulate)

(v)$AO=DO$ .....(cpct)

(vi)$CO=BO$.....(cpct)

Hence (A), and (C)