Loading [MathJax]/jax/output/HTML-CSS/jax.js

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° = 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° = 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

RSS

  1. 5th Grade Factors and Multiples | Definitions | Solved Examples | Math

    Mar 23, 25 02:39 PM

    Prime Factor of 312
    Here we will discuss how factors and multiples are related to each other in math. A factor of a number is a divisor which divides the dividend exactly. A factor of a number which is a prime number is…

    Read More

  2. Adding 2-Digit Numbers | Add Two Two-Digit Numbers without Carrying

    Mar 23, 25 12:43 PM

    Adding 2-Digit Numbers Using an Abacus
    Here we will learn adding 2-digit numbers without regrouping and start working with easy numbers to get acquainted with the addition of two numbers.

    Read More

  3. Worksheet on 12 Times Table | Printable Multiplication Table | Video

    Mar 23, 25 10:28 AM

    worksheet on multiplication of 12 times table
    Worksheet on 12 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More

  4. Vertical Subtraction | Examples | Word Problems| Video |Column Method

    Mar 22, 25 05:20 PM

    Vertical Subtraction
    Vertical subtraction of 1-digit number are done by arranging the numbers column wise i.e., one number under the other number. How to subtract 1-digit number vertically?

    Read More

  5. Worksheet on 11 Times Table | Printable Multiplication Table | Video

    Mar 22, 25 05:08 PM

    worksheet on multiplication of 11 times table
    Worksheet on 11 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home.

    Read More