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ICSE Class 9 Answered

IN the adjacent figure, ABCD is any pentagon.BP drawn parallel to AC meets DC produced at P and EQ drawn  parallel to AD meets CD produced at Q. Prove that ar ( ABCDE ) = ar ( APQ)
Asked by nisha_vini29 | 09 Mar, 2016, 10:46: AM
answered-by-expert Expert Answer
 
begin mathsize 16px style S i n c e space triangle B A P space a n d space triangle B P A space a r e space o n space t h e space s a m e space b a s e space B P space a n d space b e t w e e n space t h e space s a m e space p a r a l l e l space l i n e s space B P space a n d space A C rightwards double arrow A left parenthesis triangle B A P right parenthesis equals A left parenthesis triangle B P A right parenthesis S u b t r a c t i n g space triangle B O P space f r o m space b o t h space s i d e s comma space w e space h a v e A left parenthesis triangle B O A right parenthesis equals A left parenthesis P O C right parenthesis space space space space space space space.... left parenthesis 1 right parenthesis S i m i l a r l y comma A left parenthesis A P E right parenthesis equals A left parenthesis D P Q right parenthesis space space space space space space.... left parenthesis 2 right parenthesis N o w comma A left parenthesis triangle A P Q right parenthesis equals A left parenthesis triangle P O C right parenthesis plus A left parenthesis triangle D P Q right parenthesis plus A left parenthesis p e n t a g o n space A O C D P right parenthesis space space space space space space space space space space space space space space space space equals A left parenthesis triangle B O A right parenthesis plus A left parenthesis A P E right parenthesis plus A left parenthesis p e n t a g o n space A O C D P right parenthesis space space space space space space space space space space space space space space space space space space equals A left parenthesis p e n t a g o n space A B C D E right parenthesis end style
Answered by Rashmi Khot | 09 Mar, 2016, 12:37: PM

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