Question

Given: Angle BAC is a right angle
Angle DEC is a right angle
Line DB bisects line AE
Prove C is the midpoint of line DB

Answer 1

In two triangles i.e. triangle ABC and triangle DEC , angle BAC=angle DEC=90 degrees , angle BCA=angle DCE=vertically opposite angle, and line BC=line CD (given line DB bisects line AE). So by AAS(angle angle side) congruence condition these two triangles are congruent and hence, line BC=line DC so C is the mid point of line BD