Question

in the fig. abcd is a parallelogram and e is the mid point of side bc . if de and ab when produced meet at f, prove that af=2ab​

Answer 1



Join / Login

Class 8

>>Maths

>>Understanding Quadrilaterals

>>Parallelogram

>>In fig 14.36, ABCD is a par...

Question



In fig 14.36, ABCD is a  parallelogram and E is the mid-point of side BC. IF DE and AB when produced meet at F, prove that   AF = 2AB.





Medium

Open in App

Solution



Verified by Toppr

Solution :-

in the figure

△DCE and BFE

any DEC = any BEF (vertically opp any)

EC=BE (E is the mid point)

∠DCB=∠EBF (alternate angle DC parallel to AF)

So △DCE congruent to △BFE

Therefore DC=BF ...(1)

now CD = AB (ABCD is a parallelogram)

soAF=AB+BF

=AB+DC from (1)

=AB+AB

=2AB



Answer 2

Solution :-

in the figure

△DCE and BFE

any DEC = any BEF (vertically opp any)

EC=BE (E is the mid point)

∠DCB=∠EBF (alternate angle DC parallel to AF)

So △DCE congruent to △BFE

Therefore DC=BF ...(1)

now CD = AB (ABCD is a parallelogram)

soAF=AB+BF

=AB+DC from (1)

=AB+AB

=2AB