Question

in fig given above AB=AD angle x=angle w and angle y=angle z then prove that AP=AQ

Answer 1

given,
AB=AD,
<X=<W,
<Y=<Z
PROVE THAT AP=AQ

BY THE DIAGRAM WE CONCLUDE THAT THE FIGURE IS ROMBUS,. AS THE ANGLES ARE EQUAL

AP=AQ (: ALL EXTERIOR ANGLES ARE EQUAL)

HENCE PROVED

Answer 2

angle X = angle w given and angle y = angle Z given therefore angle X + Y = 2 angle WPF therefore angle X + Y = angle W+ Z. or angle Bac is equal to angle dAC in triangle DaC and triangle BAC. ad equals to ab given angle BAC equal to angle DAc just proved Angle B equal to angle D given and AC equals to AC common therefore Triangle Bac congruent triangle dac therefore Angle B = angle d now in triangle abp and ADq. a b equals to ad given Angle B = angle d. x = w then Triangle abp congruent ADq . ap=AQ