Triangle Classification: Analyzing Three 8-Unit Sides for Different Lengths

Triangle Classification with Equal Side Lengths

Given the values of the sides of a triangle, is it a triangle with different sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's find out if this triangle has sides that are all different lengths.
00:12 We can see from the given side lengths that this triangle is equilateral. That means all sides are equal.
00:19 Great job! And that's how we determine the type of triangle based on its sides.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the values of the sides of a triangle, is it a triangle with different sides?

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2

Step-by-step solution

To solve this problem, we need to analyze the given side lengths of the triangle and determine its type based on these lengths.

The side lengths provided are 8, 8, and 8.

According to the definitions of triangle types:

  • An equilateral triangle has all sides equal.
  • An isosceles triangle has at least two sides equal.
  • A scalene triangle has all sides different.

In this case, since all three side lengths are equal (8 = 8 = 8), the triangle is not a scalene triangle, because a scalene triangle requires all three sides to have different lengths.

Therefore, the triangle with sides 8, 8, and 8 is not a scalene triangle. The answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Classification Rule: Scalene triangles must have all three sides different
  • Recognition: Check if 8 = 8 = 8 shows equal sides
  • Verify: Count different side lengths: only 1 unique length ≠ scalene ✓

Common Mistakes

Avoid these frequent errors
  • Confusing equilateral with scalene triangle definitions
    Don't assume that any triangle with given measurements is scalene = wrong classification! Students often mix up the definitions. Always remember: scalene means ALL sides different, isosceles means TWO sides equal, equilateral means ALL sides equal.

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's the difference between equilateral, isosceles, and scalene triangles?

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Equilateral: All 3 sides equal (like 8, 8, 8)
Isosceles: Exactly 2 sides equal (like 8, 8, 5)
Scalene: All 3 sides different (like 5, 7, 9)

Why isn't this triangle scalene if it has three sides?

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Having three sides doesn't make it scalene! A scalene triangle specifically needs all three sides to be different lengths. Since all sides are 8 units, they're equal, not different.

Can a triangle be both equilateral and isosceles?

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Yes! An equilateral triangle is a special type of isosceles triangle. Since all sides are equal, it automatically has at least two equal sides, which satisfies the isosceles definition.

How do I quickly identify triangle types from side lengths?

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  • Count the different lengths:
  • 1 unique length = equilateral
  • 2 unique lengths = isosceles
  • 3 unique lengths = scalene

What if the question asks 'Is this a triangle with different sides?'

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This is asking if it's scalene. Look for the key word 'different' - it means all sides must have different measurements. If any sides are equal, the answer is No.

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