ingsameorar(ABCD) = ar(ADE)EXERCISE 9.31. In Fig.9.23, E is any point

1.	ingsameorar(ABCD) = ar(ADE)EXERCISE 9.31. In Fig.9.23, E is any point on median AD of aăIn a triangle ABC, E is the mid-point of medianatA ABC. Show that ar (ABE)ar (ACE).9.AD. Show that ar (BED)-ar(ABC)43Show that the diagonals of a parallelogram divideit into four triangles of equal area.In Fig. 9.24, ABC and ABD are two triangles onthe same base AB. If line- segment CD is bisectedby AB at O, show that ar(ABC)-ar (ABD).Fig4.
Answer» 2)In tri.ABCABD=ACD-------------(1)In tri. abd,BE is the medianAbe=bed-------------(2)now, ABD=BED=2(BED)-----------(3)ABC=ABD+ACDABC=2(ABD)-----using(1)ABC=2*2(BED)----using(3)ABC=4(BED)so, (BED)=1/4(ABC) 3)we know that diagonal of a parallelogram bisect each otherthere fore AO is equal to OCandDO is equal to OBin parallelogram ABCD AC is the diagonal and O is the median of triangle divide it into two eqaul parts of equal trianglesthis implies in triangle ABC, oc is median there fore ar(AOC)is equal to ar (BOC) (1) similarly in triangle CBD, OB is median ar(COB) is equal to ar(BOD) (2) in trianle BAD, OD is medianar(BOD) is equal to ar(AOD) (3) NOW from 1,2 and 3 we get ar(AOC)=ar(BOC)=ar(BOD)=ar(AOD)hence, prooved hit like if you find it useful

ingsameorar(ABCD) = ar(ADE)EXERCISE 9.31. In Fig.9.23, E is any point on median AD of aăIn a triangle ABC, E is the mid-point of medianatA ABC. Show that ar (ABE)ar (ACE).9.AD. Show that ar (BED)-ar(ABC)43Show that the diagonals of a parallelogram divideit into four triangles of equal area.In Fig. 9.24, ABC and ABD are two triangles onthe same base AB. If line- segment CD is bisectedby AB at O, show that ar(ABC)-ar (ABD).Fig4.

Answer»

2)In tri.ABCABD=ACD-------------(1)In tri. abd,BE is the medianAbe=bed-------------(2)now, ABD=BED=2(BED)-----------(3)ABC=ABD+ACDABC=2(ABD)-----using(1)ABC=2*2(BED)----using(3)ABC=4(BED)so, (BED)=1/4(ABC)

3)we know that diagonal of a parallelogram bisect each otherthere fore AO is equal to OCandDO is equal to OBin parallelogram ABCD AC is the diagonal and O is the median of triangle divide it into two eqaul parts of equal trianglesthis implies in triangle ABC, oc is median there fore ar(AOC)is equal to ar (BOC) (1)

similarly in triangle CBD, OB is median ar(COB) is equal to ar(BOD) (2)

in trianle BAD, OD is medianar(BOD) is equal to ar(AOD) (3)

NOW from 1,2 and 3 we get ar(AOC)=ar(BOC)=ar(BOD)=ar(AOD)hence, prooved

hit like if you find it useful

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