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CBSE Class 9 Answered

verification of angle sum property of quadrilateral
Asked by Vyom | 20 Nov, 2015, 08:10: PM
answered-by-expert Expert Answer
A n g l e space s u m space p r o p e r t y colon S u m space o f space t h e space a n g l e s space o f space a space q u a d r i l a t e r a l space i s space 360 degree. P r o o f colon 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. O b s e r v e space t h e space f o l l o w i n g space f i g u r e.
C o n s i d e r space t h e space t r i a n g l e s comma space triangle A D C space a n d space triangle A B C. B y space a n g l e space s u m space p r o p e r t y comma space w e space h a v e comma angle D A C plus angle A C D plus angle C D A equals 180 degree... left parenthesis 1 right parenthesis a n d angle B A C plus angle A C B plus angle C B A equals 180 degree... left parenthesis 2 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma angle D A C plus angle A C D plus angle C D A plus angle B A C plus angle A C B plus angle C B A equals 180 degree plus 180 degree... left parenthesis 3 right parenthesis F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space angle D A B equals angle D A C plus angle C A B... left parenthesis 4 right parenthesis angle D C B equals angle D C A plus angle A C B... left parenthesis 5 right parenthesis R e w r i t i n g space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma rightwards double arrow angle D A C plus angle B A C plus angle A C D plus angle A C B plus angle C D A plus angle C B A equals 180 degree plus 180 degree rightwards double arrow angle D A B plus angle A C D plus angle A C B plus angle C D A plus angle C B A equals 180 degree plus 180 degree space..... open square brackets F r o m space e q u a t i o n space left parenthesis 4 right parenthesis close square brackets rightwards double arrow angle D A B plus angle D C B plus angle C D A plus angle C B A equals 180 degree plus 180 degree...... open square brackets F r o m space e q u a t i o n space left parenthesis 5 right parenthesis close square brackets rightwards double arrow angle D A B plus angle D C B plus angle C D A plus angle C B A equals 360 degree T h u s space t h e space s u m space o f space t h e space a n g l e s space o f space t h e space q u a d r i l a t e r a l space i s space 360 degree
 
Answered by Vimala Ramamurthy | 21 Nov, 2015, 08:09: PM

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