In the given figure,ABparallel toCD. Prove that angleBAE -angleDCE = angleAEC  
 

Asked by Apoorv | 20th Jun, 2014, 03:05: AM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
B y space e x t e r n a l 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 B A E equals angle A E F plus angle A F E..... left parenthesis 1 right parenthesis S i n c e space A B space a n d space C D space a r e space p a r a l l e l space a n d space C E space i s space t h e space t r a n s v e r s a l comma space t h e space c o r r e s p o n d i n g space a n g l e s space a r e space e q u a l. H e n c e comma space angle A F E equals angle D C E.... left parenthesis 2 right parenthesis T h u s comma space f r o m 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 angle B A E equals angle A E F plus angle D C E rightwards double arrow angle B A E minus angle D C E equals angle A E F rightwards double arrow angle B A E minus angle D C E equals angle A E C

Answered by Vimala Ramamurthy | 20th Jun, 2014, 10:33: AM