Equilateral Triangle

High School

Definition

It is a special case of an isosceles triangle which do not only have two but three sides equal to each other. Since all three sides of an equilateral triangle are congruent, the three angles are the same that each of them is 60\(°\).

Worked examples

\(\)Side \( AB = BC = CA = 5\) cm\( \quad \angle A = \angle B = \angle C = 60^\circ\)

All three sides equal and all three angles equal to 60° — that's the defining pair of properties.

\(\)Perimeter\( = 3s = 3(8) = 24 \quad \)Area\( = \frac{s^2\sqrt{3}}{4} = \frac{64\sqrt{3}}{4} = 16\sqrt{3}\)

When one side is 8, multiply by 3 for perimeter; plug into the special area formula for equilateral triangles.

Common mistakes

An equilateral triangle has angles of \(90^\circ\), \(45^\circ\), \(45^\circ\) → All three angles are \(60^\circ\) Equilateral means equal sides AND equal angles; the angles must sum to 180°, so each is 60°.
\(\)Area\( = \frac{1}{2} \times s \times s\) → \(\)Area\( = \frac{s^2\sqrt{3}}{4}\) The base-times-height formula works, but the height is \(\frac{s\sqrt{3}}{2}\), giving the special formula.
If two sides are equal, it must be equilateral → Equilateral requires all three sides equal Two equal sides make an isosceles triangle; equilateral is the special case where the third side also matches.

Where you'll use it next

Equilateral triangles appear in trigonometry (especially the 30-60-90 reference triangle), coordinate geometry, proofs about congruence and similarity, tessellations, and real-world structures like trusses and geodesic domes.

Found in 2 StudyPug lessons

Mastering Triangle Classification: Your Key to Geometry Success

Geometry

Unlock the world of geometry by mastering triangle classification. Learn to identify and understand various triangle types, their properties, and real-world applications. Boost your problem-solving skills today!

10th Grade10th

Isosceles and equilateral triangles