in figure ap=bp xp=yp what criterion is used to show triangle apx congruent to triangle bpy
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I think the criterion used is SAS criterion of congruence.
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So in this we have to show how triangle APX is congruent to Triangle BPY
In triangle APX and triangle BPY,
AP=BP[Given]
XP= YP[ Given]
angle APX = Angle BPY [ Opposite angles are equal]
So Triangle APX is congruent to Triangle BPY by Side Angle Side ( SAS) congruency
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