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CBSE Class 9 Answered

ABCD is a rectangle.AD bisects angle B.Show that it is a square.
Asked by Vikas | 31 Jan, 2018, 12:32: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon In space Rectangle space ABCD space diagonal space straight B space bisect space angle straight B
To space prove colon space ABCD space is space straight a space square
Construction colon space Join space straight A space and space straight C. space BD space and space AC space bisect space each space other space at space straight P.
Proof colon space In space the space rectangle space diagonals space are space equal.
space space space space space space space space space space space space space space ABCD space is space straight a space parallelogram.
space space space space space space space space space space space space space space In space increment AOB space and space increment COB
space space space space space space space space space space space space space space AP equals PC
space space space space space space space space space space space space space space BP equals BP
space space space space space space space space space space space space space space angle ABO equals angle COB space space space space space space space space space space space space space space space space space space space space space space space Given
space space space space space space space space space space space space space space increment AOB space approximately equal to space increment COB space space space space space space space space space space space space space space space space space space space space space space SAS
space space space space space space space space space space space space space space AB equals BC 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 space space space space space space space space space space straight c. straight p. straight c. straight t
space space space space space space space space space space space space space space AB equals CD space and space AD equals BC space space space space space space space space space space space opposite space sides space of space rectangle
space space space space space space space space space space space space space space AB equals BC equals CD equals AD
space space space space space space space space space space space space space ABCD space is space straight a space square. end style 
Answered by Sneha shidid | 31 Jan, 2018, 01:50: PM
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