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ICSE Class 9 Answered

prove that the line joining the mid points of the parallel siodes of as trapezium divides it imto two equal parts  
Asked by ray.taxsolutions | 31 Jan, 2018, 08:19: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon space PQRS space is space straight a space trapezium. space straight M space and space straight N space are space midpoints space of space parallel space sides.
To space rove colon space straight A left parenthesis PMNS right parenthesis equals straight A left parenthesis MQRN right parenthesis
Construction colon space PA space and space QB space are space height space of space trapezium.
Assumption colon space Trapezium space is space an space isosceles space trapezium space with space PS equals QR
Proof colon space PM equals MQ space and space SN equals NR
space space space space space space space space space space space space space AN equals PM space and space MQ equals NB space space space space space opposite space sides space of space rectangle
space space space space space space space space space space space space space straight A left parenthesis PMNA right parenthesis equals straight A left parenthesis MQBN right parenthesis
space space space space space space space space space space space space space In space increment PSA space and space increment QRB
space space space space space space space space space space space space space PA equals QB
space space space space space space space space space space space space space PS equals QR
space space space space space space space space space space space space space angle PAS equals angle QBR equals 90 degree
space space space space space space space space space space space space space increment PSA space approximately equal to space increment QRB space space space space space space space space space space space space space space space space space left parenthesis RHS right parenthesis
space space space space space space space space space space space space space straight A left parenthesis PAS right parenthesis equals straight A left parenthesis QBR right parenthesis
space space space space space space space space space space space space space straight A left parenthesis PMNS right parenthesis equals straight A left parenthesis PAS right parenthesis plus straight A left parenthesis PMNA right parenthesis
space space space space space space space space space space space space space straight A left parenthesis MQRN right parenthesis equals straight A left parenthesis QBR right parenthesis plus straight A left parenthesis MQBN right parenthesis
space space space space space space space space space space space space space straight A left parenthesis PMNS right parenthesis equals straight A left parenthesis MQRN right parenthesis end style
Answered by Sneha shidid | 01 Feb, 2018, 12:57: PM

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ICSE 9 - Maths
Asked by ray.taxsolutions | 31 Jan, 2018, 08:19: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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