Question

◻ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE. 

Answer 1

Given:

◻ABCD is a parallelogram.

E is a point on side BC.

Line DE intersects ray AB in point T.

To prove: DE × BE = CE × TE

Proof: In ∆BET and ∆CED

∠BET = ∠CED   ...(Vertically opposite angles)

∠BTE = ∠CDE   ...(Alternate interior angles, AB || CD and DT is a transversal line)

By AA test of similarity,

∆BET ∼ ∆CED 

∴ `("BE")/("CE") = ("ET")/("ED")`

∴ DE × BE = CE × TE