ABCDE is a pentagon.A line through B II to AC meets DC produced at F.Show that:-
(i)ar(ACB)=ar(ACF)
(ii)ar(AEDF)=ar(ABCDE)
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OpenStudy (anonymous):
answer ma question plzzzzzzzzzzz
Directrix (directrix):
Sorry -- I don't know what "ar" as in "ar(ACB)" means. Also, I am uncertain about "produced at F." Line AC intersected line CD at point C when I drew the diagram.
OpenStudy (mridul):
ar(ACB) means area of triangle ACB
OpenStudy (anonymous):
ya
OpenStudy (mridul):
the distance between two parallel lines remains constant at every point...... so the hieght of triangles ACB and ACF is same.... and the base is common.... so the area 1/2 * AC * hieght is same.....
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OpenStudy (anonymous):
will u show me the figure
OpenStudy (mridul):
|dw:1329742406732:dw|
OpenStudy (mridul):
BF and AC are parallel... got it
???
OpenStudy (anonymous):
ya
OpenStudy (mridul):
understood 1st part???
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OpenStudy (anonymous):
ya
OpenStudy (mridul):
now for the second part.....
OpenStudy (anonymous):
k
OpenStudy (mridul):
the area of pentagon ABCDE = ar(ACDE) + ar(ABC)
but in 1st part we proved that ar(ABC)=ar(ACF)
so ar(ABCDE) = ar(ACDE) + ar(ACF) = ar(AFDE)
OpenStudy (mridul):
this is an NCERT question of class 9th i suppose
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OpenStudy (anonymous):
ya
OpenStudy (mridul):
then for the first part.... Area of triangles is same if they lie on the same base and between parallel lines....... THEorum