In figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that
(i) ar (ACB) = ar (ACF)
(ii) ar (AEDF) = ar (ABCDE)
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In figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that
(i) ar (ACB) = ar (ACF)
(ii) ar (AEDF) = ar (ABCDE)
Diagonals AC and BD of a trapezium ABCD with
intersect each other at O. Prove that ar(AOD)=ar(BOC).
The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see figure). Show that ar(ABCD)=ar(PBQR).
[Hint: Join AC and PQ. Now compare ar(ACQ) and ar(APQ)]
XY is a line parallel to side BC of a triangle ABC. If
and
meet XY at E and F respectively, show that ar(ABE)=ar(ACF).
D and E are points on sides AB and AC respectively of
such that ar (DBC) = ar (EBC). Prove that
.