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CBSE Class 9 Answered

E and F are respectively the mid points of non parallel sides AD, BC of a trapezium ABCD. Prove that EF || AB
Asked by Paresh | 20 Nov, 2015, 07:23: PM
answered-by-expert Expert Answer
 
begin mathsize 14px style J o i n space C E space a n d space p r o d u c e space i t space t o space m e e t space B A space p r o d u c e d space a t space G. I n space increment E D C space a n d space increment E A G comma angle C E D equals angle G E A space space space space space left parenthesis v e r t i c a l l y space space o p p o s i t e space a n g l e s right parenthesis angle E C D equals angle E G A space space space space space left parenthesis A l t e r n a t e space a n g l e s right parenthesis E D equals E A space space space space left parenthesis S i n c e space E space i s space t h e space m i d p o i n t space o f space A D right parenthesis T h u s comma space increment E D C approximately equal to increment E A G rightwards double arrow C D equals G A space a n d space E C equals E G space space space space left parenthesis C P C T right parenthesis I n space C G B comma E space i s space t h e space m i d p o i n t space o f space C G space a n f space F space i s space t h e space m i d p o i n t space o f space B C. rightwards double arrow B y space m i d minus p o i n t space t h e o r e m comma space E F parallel to A B end style
Answered by Rashmi Khot | 23 Nov, 2015, 08:35: AM

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CBSE 9 - Maths
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