In figure, `triangle QRS` is an equilateral triangles. Prove that,
(1) `arc RS cong arc QS cong arc QR`
(2) `m(arc QRS)=240^(@)`.

Explanation

`triangle QRS " is an equilateral triangle " " " "…….."(" Given ")`
`:. Seg RS cong seg QS cong seg QR " " "……"(" Sides of an equilateral triangle ")`
Arcs of the same circle are equal, if the related chords are congruent.
`:. arc RS cong arc QS cong arc QR`.
Let `m(arc RS)=m(arc QS)=m(arc QR)=".......(1)"`
`m(arc RS)+m(arc QS)+m(arc QR)=360^(@) " " "....."(" Measure of a circle is " 360^(@))`
`:. x+x+x=360^(@)" " "....."[" From (1) "]`
`:. 3x=360^(@)`
`:.x=(360)/(3)`
`:. x=120^(@)`
`:. m(arc RS)=m(arc QS)=m(arc QR)=120^(@)`
`m(arc QRS)=m(arc QR)+m(arc RS)" " "......"(" Arc addition postulate " )`
`:.m(arc QRS)=120^(@)+120^(@)`
`:. m(arc QRS)=240^(@)`.