1. in a quadrilateral abcd, it is given that
   (a)angles a=d
   (b)angles b=c
   (c)angles a+d=120 degree
   (d)angles c+d=180 degrees
   (e)angles a+b=180 degrees. find the measures of angles a,b,c,d
 
 
2.GIFT is a parallelogram, What kind of quadrilateral is it if :
   (a)GF=IT and GF perpendicular to IT?
    (b)GF perpendicular to IT but GF is not=IT?
   (c)GF=IT but GF is not perpendicular to IT?

Asked by ganeshbp18 | 11th Jul, 2014, 07:17: PM

Expert Answer:

1. I t space i s space g i v e n space t h a t comma space i n space a space q u a d r i l a t e r a l comma angle a equals angle d... left parenthesis 1 right parenthesis angle b equals angle c.... left parenthesis 2 right parenthesis angle a plus angle d equals 120 degree.... left parenthesis 3 right parenthesis angle c plus angle d equals 180 degree.... left parenthesis 4 right parenthesis angle a plus angle b equals 180 degree.... left parenthesis 5 right parenthesis F r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma 2 angle a equals 120 degree rightwards double arrow angle a equals 60 degree... left parenthesis 6 right parenthesis rightwards double arrow angle d equals 60 degree... left parenthesis 7 right parenthesis F r o m space e q u a t i o n s space left parenthesis 5 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space w e space h a v e comma 60 degree plus angle b equals 180 degree rightwards double arrow angle b equals 180 degree minus 60 degree rightwards double arrow angle b equals 120 degree.... left parenthesis 8 right parenthesis F r o m space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 8 right parenthesis comma space w e space h a v e comma angle c equals 120 degree T h u s comma 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 a r e : angle a equals 60 degree angle b equals 120 degree angle c equals 120 degree angle d equals 60 degree

left parenthesis 2 right parenthesis space G I F T space i s space a space p a r a l l e log r a m.

left parenthesis a right parenthesis space G F equals I T space a n d space G F perpendicular I T G F space a n d space I T space a r e space t h e space d i a g o n a l s space o f space t h e space p a r a l l e log r a m. W e space k n o w space t h a t space t h e space d i a g o n a l s space o f space a space p a r a l l e log r a m space a r e space e q u a l space i n space r e c tan g l e space a n d space s q u a r e. B u t space sin c e space G F perpendicular I T comma space t h e space g i v e n space p a r a l l e log r a m space i s space a space s q u a r e. left parenthesis b right parenthesis space G F perpendicular I T space a n d space G F not equal to I T W e space k n o w space t h a t space t h e space d i a g o n a l s space o f space a space p a r a l l e log r a m space a r e space p e r p e n d i c u l a r space i n space r h o m b u s space a n d space s q u a r e. B u t space sin c e comma space G F not equal to I T comma space t h e space g i v e n space p a r a l l l e log r a m space i s space a space r h o m b u s. left parenthesis c right parenthesis space G F equals I T space a n d space G F space i s space n o t space p e r p e n d i c u l a r space t o space I T W e space k n o w space t h a t space t h e space d i a g o n a l s space o f space a space p a r a l l e log r a m space a r e space e q u a l space i n space r e c tan g l e space a n d space s q u a r e. B u t space sin c e space G F i s space n o t space p e r p e n d i c u l a r space t o space I T comma space t h e space g i v e n space p a r a l l e log r a m space i s space a space r e c tan g l e.


Answered by Vimala Ramamurthy | 12th Jul, 2014, 06:54: PM