Triangle Classification: Is a 10-10-7 Triangle Scalene?

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

Scalene: All three sides are different lengths. Isosceles: Exactly two sides are equal. Since our triangle has sides 10, 10, and 7, it's isosceles because two sides match.

Q: Can a triangle be both isosceles and scalene?

No, never! These are mutually exclusive categories. A triangle is either scalene (all different), isosceles (two equal), or equilateral (all three equal).

Q: What if I have sides like 5, 5.0, and 3?

Be careful with decimal notation! $5 = 5.0$, so this triangle has two equal sides and is isosceles, not scalene.

Q: How do I remember which triangle type is which?

Scalene: Think 'scale' - all sides weigh differentlyIsosceles: Think 'ice-so-seal' - two sides are sealed togetherEquilateral: Equal + lateral = all sides equal

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

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00:00 Determine whether the triangle is scalene

00:03 According to the given side lengths, the triangle is isosceles

00:07 This is the solution

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 determine if the given triangle is a scalene triangle, we examine the side lengths $10$ , $10$ , and $7$ .

A triangle is classified as scalene if all three side lengths are different. Therefore, we need to check the equality between any pairs of the given side lengths:

Check if $10 = 10$ : Yes, they are equal.
Check if $10 = 7$ : No, they are not equal.
Check if $7 = 10$ : No, they are not equal.

Since the triangle has two sides of equal length ( $10$ and $10$ ), it does not satisfy the condition for being a scalene triangle.

In conclusion, the triangle is not a scalene triangle because two of its sides are equal.

Therefore, the solution to the problem is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Scalene triangles have all three sides of different lengths
Method: Compare each pair: 10 = 10 (equal), 10 ≠ 7
Check: If any two sides are equal, triangle is isosceles, not scalene ✓

Common Mistakes

Avoid these frequent errors

Assuming triangles with mostly different sides are scalene
Don't think a 10-10-7 triangle is scalene just because 10 ≠ 7! Even one pair of equal sides disqualifies it from being scalene. Always check ALL three pairs of sides - if ANY two are equal, it's isosceles, not scalene.

Practice Quiz

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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 are different lengths. Isosceles: Exactly two sides are equal. Since our triangle has sides 10, 10, and 7, it's isosceles because two sides match.

Do I need to check all three pairs of sides?

Yes! You must compare: side 1 vs side 2, side 1 vs side 3, and side 2 vs side 3. If any pair is equal, the triangle is not scalene.

Can a triangle be both isosceles and scalene?

No, never! These are mutually exclusive categories. A triangle is either scalene (all different), isosceles (two equal), or equilateral (all three equal).

What if I have sides like 5, 5.0, and 3?

Be careful with decimal notation! $5 = 5.0$ , so this triangle has two equal sides and is isosceles, not scalene.

How do I remember which triangle type is which?

Scalene: Think 'scale' - all sides weigh differently
Isosceles: Think 'ice-so-seal' - two sides are sealed together
Equilateral: Equal + lateral = all sides equal

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