Triangle Side Measurements: Determining if ABC is Equilateral

Q: Do I need to compare all three sides or just two?

You must compare all three sides! Even if the first two sides are different, you still need to check the third side. Only when all three sides are equal is it equilateral.

Q: What if two sides are equal but one is different?

That would make it an isosceles triangle, not equilateral! In this problem, all three sides (7, 10, 9) are different, so it's a scalene triangle.

Q: How can I remember the definition of equilateral?

Think of 'equi' = equal and 'lateral' = sides. So equilateral means equal sides - all three sides must be exactly the same length!

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

Equilateral: All 3 sides equalIsosceles: Exactly 2 sides equalScalene: All 3 sides different (like this triangle!)

Triangle Classification with Side Length Comparison

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

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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, these sides are not equal

00:06 Therefore the triangle is not equilateral, and this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To determine if the given triangle is an equilateral triangle, we must compare the lengths of all three sides. An equilateral triangle requires all three sides to have the same length.

Given the side lengths:

$AB = 7$
$BC = 10$
$CA = 9$

Step-by-step solution:

Step 1: Compare $AB$ with $BC$ . We see that $7 \neq 10$ . Therefore, $AB \neq BC$ .
Step 2: Compare $AB$ with $CA$ . We see that $7 \neq 9$ . Therefore, $AB \neq CA$ .
Step 3: Since $AB \neq BC$ and $AB \neq CA$ , the sides are not all equal.

Since the sides $AB$ , $BC$ , and $CA$ are not all equal, the triangle is not an equilateral triangle.

Thus, the solution to the problem is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Equilateral triangles must have all three sides equal
Technique: Compare each pair: AB = 7, BC = 10, CA = 9
Check: Since 7 ≠ 10 ≠ 9, not all sides equal ✓

Common Mistakes

Avoid these frequent errors

Only comparing two sides instead of all three
Don't just check if AB = BC and conclude it's not equilateral! You might miss that two other sides could be equal. This leads to incomplete analysis and wrong triangle classification. Always compare all three pairs: AB vs BC, AB vs CA, and BC vs CA.

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

Do I need to compare all three sides or just two?

You must compare all three sides! Even if the first two sides are different, you still need to check the third side. Only when all three sides are equal is it equilateral.

What if two sides are equal but one is different?

That would make it an isosceles triangle, not equilateral! In this problem, all three sides (7, 10, 9) are different, so it's a scalene triangle.

How can I remember the definition of equilateral?

Think of 'equi' = equal and 'lateral' = sides. So equilateral means equal sides - all three sides must be exactly the same length!

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

Equilateral: All 3 sides equal
Isosceles: Exactly 2 sides equal
Scalene: All 3 sides different (like this triangle!)

Can I use the triangle inequality to check if it's a valid triangle?

Great thinking! Yes, you should verify: 7 + 9 = 16 > 10 ✓, 7 + 10 = 17 > 9 ✓, and 9 + 10 = 19 > 7 ✓. This confirms it's a valid triangle, just not equilateral.

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