In fig 3.38 QRS is an equilateral triangle. Prove that,

(1) arc RS arc QS arc QR
(2) m(arc QRS) = 240°.



(1)Given QRS is an equilateral triangle, sides are equal in measure.
QR = RS = QS
arc QR = arc RS = arc QS [Corresponding arcs of congruent chords of a circle are congruent]
arc RS arc QS arc QR….(i)
Hence proved.
(2)m(arc RS)+ m(arc QS)+ m(arc QR) = 360˚ [Measure of a complete circle is 360°]
Also from (i) arc RS arc QS arc QR
Let m(arc RS) = x
x+x+x = 360
3x = 360
x = 120˚
m(arc QRS) = m(arc QR)+m(arc RS) [Property of sum of measures of arcs ]
m(arc QRS) = 120+120 = 240˚
Hence proved.

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