Question

pls help me with this question..
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Answer 1

✒✒✒✒ ANSWER ✒✒✒✒

Given:∥gmABCD in which O is any point inside it.

To prove:

(i) area of ΔOAB+ area of ΔOCD=1/2 area of ∥gmABCD

(ii) area of ΔOBC+ area of ΔOAD=1/2 area of ∥gmABCD

Draw POQ ∥ AB through O. It meets AD at P and BC at Q.

Proof: (i) AB∥PQ and AP∥BQ

ABQP is a ∥gm

Similarly, PQCD is a ∥ gm Now, ΔOAB and ∥gm ABQP are on same base AB and between same ∥ lines AB and PQ

ar(ΔOAB)=1/2ar(∥gmABQP)….(1)

Similarly, ar (ΔOCD)=1/2ar(∥gmPQCD)…. ( 2)

Now by adding (1) and (2) ar(ΔOAB)+ar(ΔOCD)=1/2 ar (∥gmABQP)+1/2 ar (∥gmPQCD)

=1/2[ar(∥gmABQP)+ar(∥gmPQCD)]

=1/2ar(∥gmABCD)

ar(ΔOAB)+ar(ΔOCD)=1/2ar(∥gmABCD)

Hence proved.

(ii) we know that,

ar(ΔOAB)+ar(ΔOBC)+ar(ΔOCD)+ar(ΔOAD)=ar(∥gmABCD)

[ar(ΔOAB)+ar(ΔOCD)]+[ar(ΔOBC)+ar(ΔOAD)]=ar(∥gmABCD)

1/2 ar (∥gmABCD)+ar(ΔOBC)+ar(ΔOAD)=ar(∥gmABCD)

ar (ΔOBC)+ar(ΔOAD)=ar(∥gmABCD)−1/2ar(∥gmABCD)

ar(ΔOBC)+ar(ΔOAD)=1/2ar(∥gmABCD)

Hence proved.

Answer 2

Answer:

why had the poet chosen the theme which is about one’s fight against adversity in life. In the poem of Invictus

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