Question

ABCD is a parallelogram. AD is produced to E so that DE=DC and EC produced meet AB produced in F. Prove that BF=BC.​

Answer 1

Since, ABCD is a parallelogram, therefore AB is parallel to CD.

Therefore, AF is parallel to CD.

And we can observe that EF is a traversal.

  <2=<4 (Corresponding angles)    (Equation 1)

Therefore, AE is parallel to BC.

<1=<3 So,     (Corresponding angles)   (Equation 2)

Now, in triangle DEC,

DE = DC

Therefore,

So,  <1=<2    (Equation 3) (Angles opposite to the equal opposite sides are also equal)

Therefore,  <3=<4    (By equations 1,2 and 3)

Therefore, BC = BF

Hence, proved.

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