Prove that each angle of an equilateral triangle is 60 ?

Asked by nisha_vini29 | 13th Jul, 2017, 10:19: AM

Expert Answer:

begin mathsize 16px style Given colon space
increment ABC space is space equilateral.
To space Prove colon space
angle straight A equals angle straight B equals angle straight C equals 60 degree
Proof colon
increment ABC space is space equilateral.
rightwards double arrow AB equals BC equals AC
Consider comma
AB equals BC
rightwards double arrow angle straight A equals angle straight C............. left parenthesis Angle space opposite space of space equal space sides right parenthesis.... left parenthesis straight i right parenthesis
Also comma
BC equals AC
rightwards double arrow angle straight A equals angle straight B..... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
angle straight A equals angle straight B equals angle straight C equals straight x space left parenthesis say right parenthesis
angle straight A plus angle straight B plus angle straight C equals 180 degree
3 straight x equals 180 degree
straight x equals 60 degree
angle straight A equals angle straight B equals angle straight C equals straight x equals 60 degree


end style

Answered by Sneha shidid | 13th Jul, 2017, 10:49: AM