Question

ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC andDB = DC. Prove that AD is the bisector of BC.

Answer 1

"In triangles ABC and DBC

angle A=angleD=90 degrees

AC and BD intersect each other at E

To Prove : AE x EC = ED x BE

Proof : In triangles AEB and EDC,

and AEB = DEC..............(Vertically opposite angles)

triangle ABE ~ EDC

(EB/EC) = (AE/DE)

EB x DE = EC x AE

Hence, AE x EC = ED x BE

"