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CBSE Class 9 Answered

How we prove that if each pair of opposite angles of a quadrilateral are equal then it is a parallelogram.
Asked by dimplesharma0810 | 23 Dec, 2015, 04:02: PM
answered-by-expert Expert Answer
begin mathsize 14px style L e t space A B C D space b e space a space q u a d r i l a t e r a l space i n space w h i c h space angle A equals angle C space a n d space angle B equals angle D rightwards double arrow angle A plus angle B equals angle C plus angle D N o w comma space angle A plus angle B plus angle C plus angle D equals 360 degree space left parenthesis a n g l e space s u m space p r o p e r t y right parenthesis rightwards double arrow angle A plus angle A plus angle B plus angle B equals 360 degree rightwards double arrow 2 angle A plus 2 angle B equals 360 degree rightwards double arrow 2 left parenthesis angle A plus angle B right parenthesis equals 360 degree rightwards double arrow angle A plus angle B equals 180 degree L i n e space A B space i n t e r s e c t s space A D space a n d space B C space a t space p o i n t s space A space a n d space B space r e s p e c t i v e l y space s u c h space t h a t space angle A plus angle B equals 180 degree rightwards double arrow A D parallel to B C space space angle A plus angle B equals 180 degree rightwards double arrow angle A plus angle D equals 180 degree rightwards double arrow A B parallel to C D rightwards double arrow A B C D space i s space a space p a r a l l e log r a m. end style
Answered by Rashmi Khot | 24 Dec, 2015, 09:08: AM

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