Question

Two triangles ABC and DBC are on the same base BC in which angle A=angle D=90°. If CA and BD meet each other at E, show that AE×CE =BE×DE

Answer 1

let the two triangles form a quadrilateral abcd. ac and bd are the diagonals.
now,
ac and bd intersect each other at e.
therefore,
ae x ce ......1
and
be x de .....2
from 1 and 2 we get,
ae x ce = be x de.
hope its the required answer and the required procedure.