Here we will prove that the three angles of an equilateral triangle are equal.

**Given:** PQR is an equilateral triangle.

**To prove:** ∠QPR = ∠PQR = ∠ PRQ.

**Proof:**

1. ∠QPR = ∠PQR 2. ∠PQR = ∠ PRQ. 3. ∠QPR = ∠PQR = ∠ PRQ. (Proved). |
1. Angles opposite to equal sides QR and PR. 2. Angles opposite to equal sides PR and PQ. 3. From statement 1 and 2. |

**Note:**

**1.** In the equilateral ∆PQR, let ∠PQR = ∠PRQ = ∠RPQ = x°. Therefore, 3x° = 180° as

the sum of the three angles of a triangle is 180°.

Therefore, x° = (frac{180°}{3})

⟹ x° = 60°.

Thus, each angle of an

equilateral triangle is 60°.

**2.** If one angle of an

isosceles triangle is given, the other two can be easily found out.

In the given figure, PQ =

PR.

Therefore, ∠PQR =

∠PRQ = x° (suppose).

Let ∠RPQ =

y°

Thus, y° + 2x°

= 180°, from which we get

y° = 180°

– 2x°

and x° = (frac{180° – y°}{2}).

**From The Three Angles of an Equilateral Triangle are Equal to HOME PAGE**

**Didn’t find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**