Question

Prove that, any two equilateral triangles are similar Draw figure write Given, To prove and proof slove

Answer 1

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Answer 2

Step-by-step explanation:

Given: An equilateral triangle ABC.

To Prove: ∠A = ∠B = ∠C = 60°.

Proof: ∵ ABC is an equilateral triangle

∴ AB = BC = CA ...(1)

∵ AB = BC

∴ ∠A = ∠C ...(2)

| Angles opposite to equal sides of a triangle are equal

∵ BC = CA

∴ ∠A = ∠B ...(3)

| Angles opposite to equal sides of a triangle are equal

From (2) and (3), we obtain

∠A = ∠B = ∠C ...(4)

In ∆ABC,

∠A + ∠B + ∠C = 180° ...(5)

| Sum of all the angles of a triangle is 180°

Let ∠A = x°. Then, ∠B = ∠C = x°

| From (4)

From (5),

x° + x° + x° = 180°

3x° = 180°

⇒ x° = 60°

⇒ ∠A = ∠B = ∠C = 60°.

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