Question

abcd is a parallelogram and ef parallel bd. r is the midpoint of ef. prove that be is equal to df

Answer 1

Since diagonal of a square bisects the vertex and BD is the diagonal of square ABCD

CBD=CBD=45°

 

Given : EF || BD

⇒ ∠CEF = ∠CBD = 45°  and ∠CEF = ∠CDB = 45°  (corresponding angles)

⇒ ∠CEF = ∠CFE

⇒ CE = CF    (sides opposite of equal angles are equal)    .......(1)

Now  BC = CD  (Sides of square)    ........(2)

 

Subtracting (1) from (2) we get

⇒ BC – CE = CD – CF

⇒ BE = DF