Question

QRS is an equilateral triangle. Prove : m(arc QR) = 120º​

Answer 1

Answer:

QRS is an equilateral triangle.

Proved that :

i) arc RS arc QS = arc QR

ii) m (arc QRS) = 240°.

To prove :

( i ) arc RS ≅ arc Qs ≅ arc QR

( ii ) m (arc QRS) = 240°

Given

ΔQRS is an equilateral triangle.

( i ) Finding arc RS = arc QS = arc QR :

An equilateral triangle sides are equal.

So, chord RS = chord QS = chord QR

Corresponding arc of congruent chord of circle are congruent

arc RS = arc QS = arc QR -----> (a)

Hence proved.

( ii ) Finding m (arc QRS) :

Measurement of circle is 360°.

m(arc RS) + m(arc QS) + m(arc QR) = 360° -----> (b)

From the equation (a), it has proven that arc RS = arc QS = arc QR.

So, the equation (b) becomes,

m(arc RS) + m(arc RS) + m(arc RS) = 360°

3 × m(arc RS) = 360°

m(arc RS) ={3}

360= 120°.

In m(arc QRS),

m(arc QRS) = m(arc QR) + m(arc RS)

= 120° + 120° = 240°

m(arc QRS) = 240°.

Hence proved.