Question

OA /OC=OD /OB. Prove that angle A =angle C and angle B= Angle D

Answer 1

In ∆ AOD and ∆ COB
OA/OC=OD/OB ( GIVEN)
ANGLE AOD= ANGLE BOC(VERTICALLY OPP ANGLE)
THEREFORE BY SAS SIMILARITY THEOREM ∆AOD IS SIMILAR TO TRIANGLE COB
SINCE THE TRIANGLE ARE SIMILAR ANGLE A=ANGLE C AND ANGLE B =ANGLE D

Answer 2

in triangle AOD and triangle BOC , angle aod = angle bod oa/oc=od/ob by s.a.s similarity TRIANGLE aod =TRIANGLE bod by cpct angle a =anglec similarly angle h =angle d