Question

two triangle abc and dbc are on same base bc and on same side of bc in which angle a and d are 90 . if ca and bd meet each other at e show that ae.ec =be.ed

Answer 1

Given triangles ABC and DBC are on the same base BC. Consider, Δ’s ABC and DBC ∠A = ∠D = 90° (Given) ∠AEB = ∠DEC (Vertically opposite angles are equal) Hence ΔABC ~ ΔDBC (AA similarity theorem) ∴ AE × CE = BE × DE