The Three Angles of an Equilateral Triangle are Equal

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

Given: PQR is an equilateral triangle.

The Three Angles of an Equilateral Triangle are Equal

To prove: ∠QPR = ∠PQR = ∠ PRQ.

Proof:

          Statement

1. ∠QPR = ∠PQR

2. ∠PQR = ∠ PRQ.

3. ∠QPR = ∠PQR = ∠ PRQ. (Proved).

          Reason

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.

One Angle of an Isosceles Triangle

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° = \(\frac{180° - y°}{2}\).




9th Grade Math

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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 02:45 AM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  2. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

    Jul 16, 25 02:33 AM

    Perimeter of a Figure
    Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

    Read More

  3. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 15, 25 11:46 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  4. 5th Grade Quadrilaterals | Square | Rectangle | Parallelogram |Rhombus

    Jul 15, 25 02:01 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  5. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More