Equal sides, different names

The idea

Based on equality of sides, equilateral triangles have all sides equal, isosceles triangles have two equal sides, and scalene triangles have sides of three different lengths.

How many sides can be equal?

Measure the three sides of a triangle. Some of them may have the same length.

How many of the three sides can be equal?

• None, or all three
• None, two, or all three
• Only two

Reshape the triangle

Drag A and watch the sides. Equal sides get the same tick marks. Make all three kinds.

Naming by sides

A triangle gets its name from how many of its sides are equal.

The name depends only on the lengths of the sides. It does not depend on how big the triangle is, or how it is turned.

Based on their sides, an equilateral triangle has all three sides equal, an isosceles triangle has two equal sides, and a scalene triangle has three sides of different lengths.

• Name | Its sides
• Equilateral | all three sides equal
• Isosceles | two sides equal
• Scalene | all three sides different

Notes

Based on their sides, an equilateral triangle has all three sides equal, an isosceles triangle has two equal sides, and a scalene triangle has three sides of different lengths.

Check yourself

A triangle has sides of 5 cm, 5 cm and 8 cm. What kind of triangle is it?

Which set of sides makes a scalene triangle?

Each side of an equilateral triangle is 4 cm. What is the total length of its three sides, in cm?

Answer: 12

An equilateral triangle has three equal sides: 4 + 4 + 4 = 12 cm.

Mira says: “My triangle has two equal sides, so it must be equilateral.” Is she right?

• Equilateral. An equilateral triangle needs all three sides equal. Here the third side is 8 cm.
• Isosceles — correct. Yes! Two of its sides are equal.
• Scalene. A scalene triangle has no equal sides. Here two sides are 5 cm.
• 3 cm, 4 cm and 5 cm — correct. Yes! All three lengths are different.
• 4 cm, 4 cm and 7 cm. Two sides are equal here (4 cm and 4 cm), so it is isosceles.
• 6 cm, 6 cm and 6 cm. All three sides are equal here, so it is equilateral.
• Yes. Any triangle with equal sides is equilateral.. Equilateral means all three sides are equal. Two equal sides only make it isosceles.
• No. An equilateral triangle needs all three sides equal. With only two equal it is isosceles. — correct. Yes! Two equal sides make an isosceles triangle. The third side may be different.
• Yes, but only if the third side is the longest.. The longest side does not decide it. Equilateral needs all three sides equal.