Answer 7th and 8th questions

7.  If the diagonals of a quadrilateral divide each other proportionally, prove that it is trapezium.

8 .       A B C i s   a n   i s o s c e l e s   t r i a n g l e   i n   w h i c h   A B   =   A C .   I f   B E   A C   a n d   C F     A B .   P r o v e   t h a t       ( i )     B F C   ~   C E B ( i i )       A F C   ~     A E B

7)take intersection of the diagonals as O
from draw a line parallel to any one side[say AB||OE ](AO/OC=OB/OD)-(i)
by construction
​AO/OC=AE/EC-(ii)
from(i) and (ii)
AE/EC=OB/OD
bt converse of thales theorem, 
OE|| AC
:.AB||CD
one pair of sides are parallel 
:.figure is a ||gm
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last line not ||gm trapezium
hence ,proved
 
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