Question

7. ABCD is a parallelogram. AB = a, AD=b .The mid-point of BC is E.
Find the vector AE The lines BD and AE intersect at F. Find the ratio
BF:FD. The lines DE produced and AB produced meet at the point G.
show that DG = 2DE and AG= 2AB.​

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8th

Maths

Understanding Quadrilaterals

Parallelogram

In fig 14.36, ABCD is a par...

MATHS

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.

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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