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CBSE Class 9 Answered

If the altitude drawn  from the vertices of triangle ABC  to opposite sides are equal, prove that the triangle is equilateral .
Asked by nisha_vini29 | 27 Feb, 2018, 11:37: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style In space right space triangle BEC space and space triangle BFC comma
BC space equals space BC space left parenthesis common right parenthesis
BE equals CF space space space left parenthesis given right parenthesis
rightwards double arrow triangle BEC space approximately equal to space triangle BFC space space left parenthesis RHS space congruence right parenthesis
rightwards double arrow angle straight B equals angle straight C space space space space left parenthesis cpct right parenthesis
rightwards double arrow AC equals AB space space space left parenthesis sides space opposite space to space equal space angles space are space equal right parenthesis space space space.... left parenthesis straight i right parenthesis
Similarly comma space triangle BEC approximately equal to triangle BFC
rightwards double arrow angle straight B equals angle straight A
rightwards double arrow AC equals BC space.... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma
AB equals AC equals BC
rightwards double arrow ABC space is space an space equilateral space triangle. end style
Answered by Rashmi Khot | 28 Feb, 2018, 12:43: PM
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