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Question -

In the given figure, CD || AE and CY || BA.
(i) Name a triangle equal in area of ΔCBX
(ii) Prove that ar (Δ ZDE) = ar (Δ CZA)
(iii) Prove that ar (BCZY) = ar (Δ EDZ).



Answer -

Given:
(1) CD||AE.
(2) CY||BA.
To find:
(i) Name a triangle equal in area of CBX.
(ii)  .
(iii)  .
Proof:
(i) Since triangle BCY and triangle YCA are on the same base and between same parallel, so their area should be equal. Therefore
 
Therefore area of triangle CBX is equal to area of triangle AXY
(ii) Triangle ADE and triangle ACE are on the same base AE and between the same parallels AE and CD.
 
(iii) Triangle ACY and BCY are on the same base CY and between same parallels CY and BA. So we have
 
Now we know that
 

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