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
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