Question

abcd is a parallelogram. the sides ab and ad are produced to e and f respectively, such that ab=be and ad=df. prove that triangle bec congruent to triangle dcf

Answer 1

Hey friend here is your answer:
Given: abcd is a parallelogram and ab= be, ad=df.
Now, dc=ab
But ab= be
Therefore, dc=be.......1
Similarly,
bc=ad
But ad=df
Therefore, df= bc.... 2
Now in triangles bce and dfc respectively, two sides are equal
Therefore their equal and opposite sides are also equal. So, angle bce= angle bec and angle dfc =angle dcf
Therefore, angle cbe= angle fdc...... 3
From equations 1,2&3:triangle bce is congruent to triangle dfc
From side angle side congruency
Hence proved
☺ hope it helps☺

Answer 2

Hope it will help you