Triangle Classification: Identifying a Triangle with AB = BC

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

An isosceles triangle has exactly 2 equal sides, while an equilateral triangle has all 3 sides equal. Since we only know AB = BC (2 sides), this is isosceles.

Q: Could this triangle also be equilateral?

It could be, but we don't have enough information! We'd need to know that AB = BC = AC to call it equilateral. With only AB = BC given, we can only say it's isosceles.

Q: What if the triangle looks like it has a right angle?

A triangle can be both isosceles and right-angled! The classification by sides (isosceles) is separate from classification by angles (right triangle).

Q: How do I remember the triangle types?

Scalene: No equal sidesIsosceles: 2 equal sidesEquilateral: 3 equal sidesThink: Iso = two, Equi = equal all!

Triangle Classification with Equal Side Properties

Look at the triangle below.

AB = BC

What type of triangle is it?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the triangle below.

AB = BC

What type of triangle is it?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the properties of triangles to classify it

Now, let's work through each step:
Step 1: The triangle is given with sides $AB$ and $BC$ equal in length.
Step 2: According to the properties of triangles, a triangle with at least two equal sides is classified as an isosceles triangle.
Therefore, given that $AB = BC$ , the triangle is an Isosceles triangle.

Therefore, the solution to the problem is Isosceles.

Final Answer

Isosceles

Key Points to Remember

Essential concepts to master this topic

Definition: Triangles with two equal sides are called isosceles triangles
Recognition: When AB = BC, identify the two equal sides first
Verification: Check that exactly two sides are equal, not all three ✓

Common Mistakes

Avoid these frequent errors

Confusing isosceles with equilateral triangles
Don't assume AB = BC means all three sides are equal = calling it equilateral! This ignores that only two sides are given as equal. Always check how many sides are equal: two sides = isosceles, three sides = equilateral.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

What's the difference between isosceles and equilateral triangles?

An isosceles triangle has exactly 2 equal sides, while an equilateral triangle has all 3 sides equal. Since we only know AB = BC (2 sides), this is isosceles.

Could this triangle also be equilateral?

It could be, but we don't have enough information! We'd need to know that AB = BC = AC to call it equilateral. With only AB = BC given, we can only say it's isosceles.

What if the triangle looks like it has a right angle?

A triangle can be both isosceles and right-angled! The classification by sides (isosceles) is separate from classification by angles (right triangle).

How do I remember the triangle types?

Scalene: No equal sides
Isosceles: 2 equal sides
Equilateral: 3 equal sides

Think: Iso = two, Equi = equal all!

Does the position of the triangle matter?

No! Whether the triangle is upright, sideways, or upside down doesn't change its classification. Only the side lengths matter for determining if it's scalene, isosceles, or equilateral.

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