Data: To Construct an equilateral triangle, given its side.
Steps of Construction :
1. Construct AB = 6 cm.
2. With A as centre and convenient scale draw an arc, it meets AB at P.
3. With P as centre, with same radius draw an arc, it intersects first arc at Q, AQ is joined and produced. ∠QAB = 60°.
4. With A as centre and taking 6 cm radius draw an arc. It intersects at C which is produced line of AQ.
5. Next, BC is joined, ABC is an equilateral triangle.
In ∆ABC, ∠A = ∠B = ∠C = 60°
AB = BC = CA = 6 cm.
In ∆ABC, AB = AC = 6 cm.
∠A = 60° ∠B = 60°
∠A + ∠B + ∠C = 180°
60 + ∠B + ∠B =180 (∵ ∠B = ∠C)
60 + 2∠B = 180
2∠B = 180 – 60
2∠B = 120°
∴ ∠B = \(\frac{120}{2}\)
∴ ∠B = 60°
∴∠B = ∠C = 60°
∴∠A = ∠B = ∠C = 60°
AC = BC (Opposite sides of equal angles)
But, AB = AC (known)
∴ AB = BC = CA = 6 cm.
