Question

prove that each angle of an equilateral triangle is 60°​

Answer 1

Refer to the attachment for diagram.

Its simple,

First we know that all sides of equilateral triangles are equal,

=> AB = BC = AC.

Now for sides AB and BC,

AB = BC ( GIVEN)

L A = L C ( angles opposite to equal sides are equal )..........(1)

Now for sides AB and AC,

AB = AC ( GIVEN)

L C = L B ( angles opposite to equal sides are equal )........(2)

Now for sides AC and BC,

AB = BC ( GIVEN)

L A = L B ( angles opposite to equal sides are equal ) ....... (3)

From (1), (2) and (3),

L A = L B = L C

Thus, in triangle ABC,

L A + L B + L C = 180⁰ ( Angle sum property of triangle )

( put, L B = L C = L A)

=> L A + L A + L A = 180⁰

=> 3L A = 180⁰

$= > <em>L</em><em> </em>A = \frac{180}{3}$

thus, L A = 60⁰

therefore, L A = L B = L C = 60⁰

Hence proved.