Question

point O is taken inside of an equal side of a quadilateral ABCD ,all sides are eual such that OB = OD, show that A,O and C are collinear.​

Answer 1

Answer:

ao and oc are in straight line

Step-by-step explanation:

consider triangles DOC and BOC

DO = BO (given)

DC = BC (since all sides are equal)

OC = OC ( common)

by SSS congruency criterion,they are congruent

so, angle DOC = angle BOC ( CPCT ). ----------------1

consider triangles ADO and ABO

DO = OB ( given )

AD = AB ( since all sides are equal )

AO = AO ( common )

by SSS congruency criterion, they are congruent

so, angle AOD = angle AOB (CPCT). --------------------2

angle AOD + angle AOB + angle DOC + angle BOC = 360°(angle at a point is 360°

from 1 and 2,

angle AOD + angle AOD + angle DOC + angle DOC = 360°

2 angle AOD + 2 angle DOC = 360°

2( angle AOD + angle DOC) = 360°

angle AOD + angle DOC = 180°

so they form a linear pair

therefore, AO and OC are in one and the same straight line.