Question

in the adjoining figure,BM and DM are perpendiculars to the line segment AC.If BM=DM,prove that A.C. insects BD.

Answer 1

In triangle BME and triangle DNE
BM=DN (given)
Angle DNE= Angle BME (each90)
Angle DEN= Angle BEM (vertically opposite angles)
therefore triangle BME= triangle DNE (AAS)
so AC=BD (cpct)
therefore AC bisects BD