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som dutt
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Asked: 2023-03-28T03:45:56+00:00 In:

Show that the angles of an equilateral triangle are 60° each.

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Show that the angles of an equilateral triangle are 60° each.

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.

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      Show that the angles of an equilateral triangle are 60° each.

      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°.

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