ABC and DBC are two triangles on the same base BC.and on the same side of BC with angle A=angleD=90 degrees. if CA and BD meet each other at E. Show that AE*EC=BE*ED

Hello student,
Please find the answer to your question below
Given : 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

Hello student,
Please find the answer to your question below
Given : 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