Question
Wed March 11, 2015 By: Rishabh Shakya

In the given figure, ABCD is a rectangle and X and Y are points on sides AD and BC respectively such that AY=BX. show that angleABX=BAY

Expert Reply
Vimala Ramamurthy
Wed March 11, 2015
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.
A B C D space i s space a space r e c tan g l e. space L e t space X space a n d space Y space b e space t w o space p o i n t s space s u c h space t h a t space A Y equals B X N o w space 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 B X space a n d space triangle B A Y angle X A B equals angle Y B A equals 90 degree space space space space space space open square brackets r i g h t space a n g l e close square brackets A Y equals B X space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets g i v e n close square brackets A B equals B A space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets c o m m o n space s i d e close square brackets T h u s comma space b y space R i g h t space A n g l e minus H y p o t e n u s e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e comma space w e space h a v e comma triangle A B X approximately equal to triangle B A Y T h u s space c o r r e s p o n d i n g space p a r t s space o f space t h e space c o r r e s p o n d i n g space t r i a n g l e s space a r e space c o n g r u e n t. B y space c p c t comma space A Y equals B X comma space a n d space angle A B X equals angle B A Y
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