Define the same as each of the other two angles in the equilateral triangle.
NCERT Books for Session 2022-2023 are based on CBSE Board.
Important Triangles Solutions for class 9th Exercise 7.2, Question no: 8.
Show that the angles of an equilateral triangle are 60° each.
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In ΔABC,
AB = AC [∵ Given]
∠C = ∠B …(1) [∵ Angles opposite to equal sides are equal]
Similarly,
In ΔABC,
AB = BC [∵ Given]
∠C = ∠A …(2) [∵ Angles opposite to equal sides are equal]
From the equation (1) and (2), we have
∠A = ∠B = ∠C …(3)
In ΔABC,
∠A + ∠B + C = 180°
⇒ ∠A +∠A+ ∠A= 180° [∵ From the equation (3)]
⇒ 3∠A = 180°
⇒ ∠A = (180°/3) = 60°
Hence, ∠A = ∠B = ∠C = 60°.