Question

Answer 2 on of this question

Answer 1

Answer:

 constructing a line parallel to DC and AB through point p  say ST

• ar(APB) = 1/2ar(ABTS)         (same base AB and between same parallel AB and ST)      - equation 1
• ar(PDC) = 1/2ar(DCTS)          (same base DC and between same parallel  DC and ST)     - equation 2
• adding equation 1 and 2              we get    
•         ar(APB)+ar(PDC) = 1/2(ABCD)      -equation 3                                                                                                            .....................from proof we know (i)............................
•           ar(APD)+ar(PBC) = 1/2(ABCD)            -equation 4
• form equation 3 and 4  ar(APD)+ar(PBC) = ar(APB)+ar(PDC)                                                                                       HENCE THE PROOF