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CBSE Class 9 Answered

State and prove converse of mid-point theorem. 
Asked by Rishank | 12 Feb, 2016, 10:31: PM
answered-by-expert Expert Answer
C o n v e r s e space o f space m i d p o i n t space t h e o r e m colon T h e space l i n e space t h r o u g h space t h e space m i d p o i n t space o f space o n e space s i d e space o f space a space t r i a n g l e comma space w h e n space d r a w n space p a r a l l e l space t o space a space s e c o n d space s i d e comma space b i s e c t s space t h e space t h i r d space s i d e. P r o o f colon L e t space A B C space b e space a space t r i a n g l e space s u c h space t h a t space D space i s space t h e space m i d p o i n t space o f space t h e space l i n e space A B. space L e t space E space b e space a space p o i n t space o n space t h e space l i n e space A C comma space s u c h space t h a t space D E space parallel to space B C. space space I f space p o s s i b l e comma space l e t space u s space a s s u m e space t h a t space E space i s space n o t space t h e space m i d p o i n t space o f space t h e space l i n e space A C. space L e t space E apostrophe space b e space t h e space m i d p o i n t space o f space t h e space l i n e space A C. space L e t space u s space d r a w space a space l i n e space D E apostrophe. space space N o w space i n space triangle A B C comma space D E apostrophe space i s space t h e space l i n e space j o i n i n g space t h e space m i d p o i n t s space o f space t h e space l i n e s space A B space a n d space A C. space T h e r e f o r e comma space b y space M i d p o i n t space t h e o r e m comma space D E apostrophe space parallel to space B C. space space B u t space w e space h a v e space D E space parallel to space B C. space T h i s space i s space a space c o n t r a d i c t i o n comma space a s space o n l y space a space u n i q u e space l i n e space c a n space p a s s space t h r o u g h space t h e space p o i n t space D space w h i c h space i s space p a r a l l e l space t o space t h e space l i n e space B C. space space H e n c e comma space E space i s space t h e space m i d p o i n t space o f space t h e space l i n e space A C comma space i. e. comma space l i n e space D E space b i s e c t s space t h e space s i d e space A C. space left parenthesis P r o v e d right parenthesis
Answered by satyajit samal | 15 Feb, 2016, 12:13: PM

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CBSE 9 - Maths
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