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Show that the Angles of an Equilateral Triangle Are 60º Each. - CBSE Class 9 - Mathematics

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Question

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

Solution

Let us consider that ABC is an equilateral triangle.

Therefore, AB = BC = AC

AB = AC

⇒ ∠C = ∠B (Angles opposite to equal sides of a triangle are equal)

Also,

AC = BC

⇒ ∠B = ∠A (Angles opposite to equal sides of a triangle are equal)

Therefore, we obtain

∠A = ∠B = ∠C

In ΔABC,

∠A + ∠B + ∠C = 180°

⇒ ∠A + ∠A + ∠A = 180°

⇒ 3∠A = 180°

⇒ ∠A = 60°

⇒ ∠A = ∠B = ∠C = 60°

Hence, in an equilateral triangle, all interior angles are of measure 60º.

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APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 7: Triangles
Ex. 7.20 | Q: 8 | Page no. 124

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Solution Show that the Angles of an Equilateral Triangle Are 60º Each. Concept: Properties of a Triangle.
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