my doubt is if there is a rhombus ABCD and we draw a diagnol AC will this diagnol bisect angles A and C.

Asked by kiranq6 | 12th Nov, 2015, 09:59: AM

Expert Answer:

L e t space u s space c o n s i d e r space t h e space p r o p e r t i e s space o f space a space r h o m b u s colon 1. space A l l space t h e space s i d e s space o f space t h e space r h o m b u s space a r e space c o n g r u e n t. 2. space O p p o s i t e space s i d e s space a r e space p a r a l l e l space a n d space e q u a l 3. space O p p o s i t e space a n g l e s space a r e space e q u a l space a n d space a d j a c e n t space a n g l e s space a r e space s u p p l e m e n t a r y. 4. space D i a g o n a l s space p e r p e n d i c u l a r l y space b i s e c t space e a c h space o t h e r. 5. space D i a g o n a l s space a r e space t h e space a n g l e space b i s e c t o r s. 6. space D i a g o n a l s space d i v i d e space t h e space r h o m b u s space i n t o space f o u r space c o n g r u e n t space r i g h t space t r i a n g l e s.  S i n c e space A B C D space i s space a space r h o m b u s comma space i t space f o l l o w s space t h e space a b o v e space p r o p e r t i e s. A n d space w e space h a v e comma space A C space a s space t h e space d i a g o n a l. H e n c e space b y space p r o p e r t y space 5 comma space A C space i s space t h e space a n g l e space b i s e c t o r space o f space a n g l e s space A space a n d space C. A n d comma space B D space i s space t h e space a n g l e space b i s e c t o r space o f space a n g l e s space B space a n d space D.

Answered by Vimala Ramamurthy | 13th Nov, 2015, 08:42: AM