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

RSS

  1. Estimating Sums and Differences | Estimations | Practical Calculations

    Jan 12, 25 01:47 PM

    Estimating Difference
    For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is requir…

    Read More

  2. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jan 12, 25 01:36 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  3. Checking Subtraction using Addition |Use Addition to Check Subtraction

    Jan 12, 25 01:13 PM

    Checking Subtraction using Addition Worksheet
    We can check subtraction by adding the difference to the smaller number. Since the sum of difference and smaller number is equal to the larger number, subtraction is correct.

    Read More

  4. Worksheet on Subtraction of 4-Digit Numbers|Subtracting 4-Digit Number

    Jan 12, 25 09:04 AM

    Worksheet on Subtraction of 4-Digit Numbers
    Practice the questions given in the worksheet on subtraction of 4-digit numbers. Here we will subtract two 4-digit numbers (without borrowing and with borrowing) to find the difference between them.

    Read More

  5. Subtraction of 4-Digit Numbers | Subtract Numbers with Four Digit

    Jan 12, 25 08:41 AM

    Properties of Subtraction of 4-Digit Numbers
    We will learn about the subtraction of 4-digit numbers (without borrowing and with borrowing). We know when one number is subtracted from another number the result obtained is called the difference.

    Read More