Triangle Side Analysis: Verifying Equilateral Properties with 6-Unit Sides

Triangle Classification with Equal Side Measurements

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

AAACCCBBB6

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether the triangle is equilateral
00:03 According to the given side lengths, the triangle is equilateral
00:06 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

AAACCCBBB6

2

Step-by-step solution

To determine if the triangle is equilateral, we need to verify if all three sides are of equal length. The given side lengths are:

  • AB=6 AB = 6
  • BC=6 BC = 6
  • CA=6 CA = 6

An equilateral triangle is one in which all sides are equal. Thus, we check the equality:

AB=BC=CA AB = BC = CA .

Substituting the given values, we have:

  • 6=6=6 6 = 6 = 6

Since all three sides of the triangle are indeed equal, we conclude that the triangle is an equilateral triangle.

Therefore, the correct answer is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Equilateral triangles have all three sides exactly equal
  • Method: Compare each side length: AB = 6, BC = 6, CA = 6
  • Verification: Check that 6 = 6 = 6 confirms equilateral classification ✓

Common Mistakes

Avoid these frequent errors
  • Assuming visual appearance determines triangle type
    Don't rely on how the triangle looks in the diagram = wrong conclusions! Visual drawings can be misleading or not drawn to scale. Always compare the actual numerical measurements of all three sides to classify triangles correctly.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

What if two sides are equal but one is different?

+

That would make it an isosceles triangle, not equilateral! An isosceles triangle has exactly two equal sides, while equilateral requires all three sides to be equal.

Do the angles matter for identifying equilateral triangles?

+

If all sides are equal, the angles are automatically equal too (each 60°). But for identification, just check the side lengths - that's the quickest method!

What if the sides are 6.0, 6, and 6.00?

+

These are all equal! 6.0 = 6 = 6.00 - different decimal representations don't change the value. The triangle is still equilateral.

How precise do the measurements need to be?

+

In math problems with exact values like this, they must be exactly equal. In real-world measurements, very small differences might be due to measurement error.

Can negative side lengths make an equilateral triangle?

+

No! Side lengths must always be positive numbers. Negative lengths don't make sense for actual distances in geometry.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations