Triangle Side Analysis: Is an 8-8-5 Triangle Scalene?

Q: What's the difference between scalene and isosceles triangles?

Scalene: All three sides have different lengths. Isosceles: Exactly two sides are equal. Since this triangle has sides 8, 8, and 5, it's isosceles because two sides are equal.

Q: How do I quickly identify triangle types by side lengths?

Follow this checklist: All sides equal = EquilateralTwo sides equal = IsoscelesAll sides different = Scalene

Q: Can a triangle have sides 8-8-5 and still be valid?

Yes! Check the triangle inequality: each side must be less than the sum of the other two. Here: 8

Q: Why does the diagram show the triangle if it's not scalene?

The diagram helps you visualize the triangle and see the side lengths clearly. The question asks whether it's scalene (all different sides) - and the answer is no because two sides are equal.

Q: What if I accidentally said 'yes' to this question?

That's a common mistake! Remember: the question asks if it has all different sides. Since 8 = 8, not all sides are different, so the answer must be No.

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 the triangle is scalene. A scalene triangle has all sides of different lengths.

00:14 Based on the side lengths given, this triangle is not scalene. It is actually an isosceles triangle, which means it has two sides that are the same length.

00:24 And that's how you determine the type of triangle using side lengths!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To solve this problem, we will examine the side lengths of the triangle:

Step 1: Identify each side: $a = 8$ , $b = 5$ , $c = 8$ .
Step 2: Compare the sides:

$a = c$ because both sides are $8$ units. This means side $a$ is equal to side $c$ .

This information indicates that the triangle is not scalene because at least two sides are equal.

Therefore, the triangle is not a triangle with all different sides. It is an isosceles triangle because it has exactly two equal sides.

The correct response to the question "Given the values of the sides of a triangle, is it a triangle with different sides?" is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Scalene triangles have all three sides of different lengths
Technique: Compare each pair: 8 ≠ 5, but 8 = 8
Check: If any two sides are equal, triangle is not scalene ✓

Common Mistakes

Avoid these frequent errors

Confusing scalene with isosceles triangle definitions
Don't assume a triangle with two equal sides is scalene = wrong classification! Students often mix up that scalene means ALL different sides, not just some. Always check if ANY two sides are equal - if yes, it's isosceles, not scalene.

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 scalene and isosceles triangles?

Scalene: All three sides have different lengths. Isosceles: Exactly two sides are equal. Since this triangle has sides 8, 8, and 5, it's isosceles because two sides are equal.

How do I quickly identify triangle types by side lengths?

Follow this checklist:

All sides equal = Equilateral
Two sides equal = Isosceles
All sides different = Scalene

Can a triangle have sides 8-8-5 and still be valid?

Yes! Check the triangle inequality: each side must be less than the sum of the other two. Here: 8 < 8+5 ✓, 8 < 8+5 ✓, and 5 < 8+8 ✓

Why does the diagram show the triangle if it's not scalene?

The diagram helps you visualize the triangle and see the side lengths clearly. The question asks whether it's scalene (all different sides) - and the answer is no because two sides are equal.

What if I accidentally said 'yes' to this question?

That's a common mistake! Remember: the question asks if it has all different sides. Since 8 = 8, not all sides are different, so the answer must be No.

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