Question

In a triangle ABC , D and E are midpoints of the sides AB, AC . Through E , a straight line is drawn parallel to AB and meet BC at F. Prove that BDEF is a parallelogram​

Answer 1

Step-by-step explanation:

In ΔABC,

 

F is the mid-point of BC (BF = CF)

E is the mid-point of CA  (AE = CE)

 

∴FE || AB (Using BPT)

⇒FE || BD .........(1)

 

D is the mid-point of AB  (AD = BD)

E is the mid-point of CA  (AE = CE)

 

∴DE || BC (Using BPT)

⇒DE || BF ..........(2)

From equations (1) and (2), we get,

BDEF is a parallelogram.

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