Triangle Classification: Identifying the Type When AB = AC = BC

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

Equilateral means all 3 sides are equal, while isosceles means only 2 sides are equal. Since AB = AC = BC shows all three sides equal, this is equilateral!

Q: Are all angles in this triangle also equal?

Yes! In an equilateral triangle, all angles are 60 degrees each. Equal sides always mean equal angles in triangles.

Q: Could this triangle be called isosceles too?

Technically yes, since it has at least two equal sides. But we use the most specific name available - equilateral is more precise than isosceles.

Q: How do I remember the triangle types?

Think of it like this: Scalene = no equal sidesIsosceles = 2 equal sidesEquilateral = 3 equal sides (most special!)

Q: What if the diagram doesn't look perfectly equal?

Always trust the given information over visual appearance! The problem states AB = AC = BC, so it's equilateral regardless of how the drawing looks.

Triangle Classification with Equal Side Lengths

Look at the triangle below.

AB = AC = BC

What type of triangle is it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's figure out what kind of triangle we have here.

00:09 Given information tells us that all sides are equal.

00:13 When a triangle's sides are all equal, each angle is sixty degrees.

00:18 And a triangle with all equal sides is called an equilateral triangle.

00:23 That's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the triangle below.

AB = AC = BC

What type of triangle is it?

Step-by-step solution

To classify the triangle, observe that all three sides are equal as given by $AB = AC = BC$ . This equality of all three sides fits the definition of an equilateral triangle, which is a triangle where all sides have the same length.

Thus, the type of triangle is equilateral.

Final Answer

Equilateral

Key Points to Remember

Essential concepts to master this topic

Definition: When all three sides are equal, triangle is equilateral
Technique: Check if AB = AC = BC means all sides identical
Verification: Count equal sides: three equal sides = equilateral triangle ✓

Common Mistakes

Avoid these frequent errors

Confusing equilateral with isosceles triangles
Don't call a triangle with all equal sides 'isosceles' = wrong classification! Isosceles means only TWO sides equal. Always remember: three equal sides = equilateral, two equal sides = isosceles.

Practice Quiz

Test your knowledge with interactive questions

Can a triangle have a right angle?

FAQ

Everything you need to know about this question

What's the difference between equilateral and isosceles?

Equilateral means all 3 sides are equal, while isosceles means only 2 sides are equal. Since AB = AC = BC shows all three sides equal, this is equilateral!

Are all angles in this triangle also equal?

Yes! In an equilateral triangle, all angles are 60 degrees each. Equal sides always mean equal angles in triangles.

Could this triangle be called isosceles too?

Technically yes, since it has at least two equal sides. But we use the most specific name available - equilateral is more precise than isosceles.

How do I remember the triangle types?

Think of it like this:

Scalene = no equal sides
Isosceles = 2 equal sides
Equilateral = 3 equal sides (most special!)

What if the diagram doesn't look perfectly equal?

Always trust the given information over visual appearance! The problem states AB = AC = BC, so it's equilateral regardless of how the drawing looks.

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