Question

A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D and B are equal. show that AO and OC are in one and same straight line

Answer 1

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.


happy that I could come to some help to you xD

Answer 2

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