Question

BP is perpendicular AC ,DQ is perpendicular BP and BP=DQ. prove that AC bisects BD​

Answer 1

Answer:

ABCD is a Rectangle , AC is the diogonal, BP and DQ are perpendiculars to the diogonal AC,

Another diogonal BD is drawn here, AC bisects BD in the point R,

now In triangle BPR and triangle DQR:-----

1) angle BPR = angle DQR ( 90°)

2) angle BRP = angle DRQ ( vertically opposite)

3) BR = DR (AC bisects BD at point R),.

therefore triangle BRP congruent to triangle DQR,( ASA),

therefore, BP = DQ.