Question

prove that each angle of an equivalent triangle measures 60 degree

Answer 1

Fig. is given on picture...

now,

★ GIVEN : triangle ABC is an equilateral triangle.
so, AB = BC = AC (all sides of equilateral triangle are equal).

★ TO PROVE : angle A = angle B =
angle C = 60°

★ PROOF :
as, AB = AC (given)
→ Angle C = angle B ( angles opposite to equal sides are equal) – (1)

similarly, AC = BC (given)
→ Angle B = angle A ( angles opposite to equal sides are equal) – (2)

so, from (1) & (2), we get...

Angle A = Angle B = angle C – (3)

angle A + Angle B + Angle C = 180° ( angle sum property of a triangle)

→ angle A + angle A + angle A = 180° [from (3)]
→ 3(angle A) = 180°
→ A = 180°/3
→ A = 60°

so, Angle A = Angle B = angle C = 60°
hence proved...