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In the figure , `Delta QRS ` is an equilateral triangle. Prove that (1) arc RS `~= arc QS ~= ` arc QR (2) m (arc QRS ) `= 240^(@)`. Proof `:` |
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Answer» `Delta QRS ` is an equilateral triangle ….(Given ) `:.` seg RS `~= ` seg QS `~=` seg QR …(Sides of equilateral triangle ) Arcs of the same circle are equal, if the related chords are congruent. `:. ` arc RS `~=` arc QS `~=` arc QR ....(1) Let m(arc RS ) = m (arc QS ) = m (arc QR ) = x m ( arc RS ) + m (arc QS ) + m ( arc QR ) ` = 360^(@)` ....( Measure of the 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 0 + m (arc RS ) ....(Arc addition postulate ) `:.` m ( arc QRS ) `= 120 ^(@) + 120^(@)` `:.` m ( arc QRS ) = `240^(@)` |
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