Question

in the figure ABCD is a paralleogram and E is the mid -point of side BC. If DE and AB when prouduced meet at F ,prove that AF=2AB​

Answer 1

Answer:

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF=2AB

Answer 2

Step-by-step explanation:

Given,

ABCD is a parallelogram so, AB=DC

Also CE=BE (E is the midpoint)

To prove - AF=2AB

Proof -

In triangle DCE and triangle BEF

angle DEC = angle BEF

CE=BE

angle DCE =angle EBF (alt. interior angles )

By ASA triangle DEC ~ triangle BEF

then DC=BF=AB

now,

AF = AB + BF

AF = AB +AB

AF=2AB (Hence proved)