Question

OX bisects $\angle AOB$. C is any point on OX. If $CD\perp OA$ and $CE\perp OB$, then which of the following is true?

• A. $△COD\cong △COE$ by AAS postulate
• B. $△COD\cong △COE$ by RHS postulate
• C. $△COD\cong △COE$ by ASA postulate
• D. CO = DO = EO

Answer 1

The correct option is A $△COD\cong △COE$ by AAS postulate

In $△OCD$ and $△OCE$

(i) $\angle COD=\angle COE$ ......(given)

(ii) $\angle CDO=\angle CEO={90}^{\circ }$......(given)

(iii) OC = OC ......(common)

$\therefore △COD\cong △COE$ ....(AAS Postulate)

$\Rightarrow$ CD = CE and DO = EO....(CPCT)