Question

A point P is taken inside an equilateral four sided figure such that its distance from the angular
points B and D are equal. Show that AP and PC are in one and the same straight line.​

Answer 1

Answer:

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 of some help to you xD

Answer 2

Answer:

bro this is answer right