An isosceles triangle is a triangle with at least two sides of equal length. The equal sides are called legs, and the third side is the base. The two angles touching the base, the base angles, are always equal. If the angle between the legs is 40 degrees, each base angle is 70 degrees.
Fold an isosceles triangle along its dashed line and the two halves match, which is why the base angles are equal.
Formal definition and notation
Triangle ABC is isosceles if at least two of its sides are congruent, say AC = BC. The angle between the congruent sides (∠ C) is the vertex angle, and ∠ A and ∠ B are the base angles. The Isosceles Triangle Theorem states that the base angles are congruent; its converse states that a triangle with two congruent angles is isosceles.
All three sides and angles are equal (60° each). An isosceles triangle needs only two equal sides, like 6, 6, 10.
Isosceles Trianglevs.Scalene triangle
A scalene triangle has no equal sides and no equal angles, such as sides 4, 6, 7.
Quick check: 3 questions
Question 1 of 3
An isosceles triangle has base angles of 75°. What is the vertex angle?
Show answer and explanation
Answer: B.180° − 75° − 75° = 30°. 105° subtracts only one base angle, 75° assumes all angles are equal, and 15° is 90 − 75.
Question 2 of 3
Which side lengths make an isosceles triangle?
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Answer: C. 6, 6, 9 has two equal sides and satisfies the triangle inequality (6 + 6 > 9). 2, 2, 5 has equal sides but 2 + 2 < 5, so it cannot close into a triangle. 3, 4, 5 and 7, 8, 9 are scalene.
Question 3 of 3
The vertex angle of an isosceles triangle is 90°. What are the base angles?
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Answer: D.(180° − 90°) ÷ 2 = 45°. This is the 45-45-90 right triangle. 30° and 60° are unequal, 60° each would need a 60° vertex, and two more right angles are impossible.
Isosceles Triangle: frequently asked questions
What makes a triangle isosceles?
Having at least two sides of the same length. Equivalently, having at least two equal angles: if two angles of a triangle are equal, the sides opposite them are equal too. So a triangle with angles 50°, 50°, 80° is isosceles even if no side lengths are given.
Can an isosceles triangle be a right triangle?
Yes. If the vertex angle is 90°, the two base angles are each 45°, giving the isosceles right triangle, also called the 45-45-90 triangle. Its legs are equal and its hypotenuse is √2 times a leg. A base angle can never be the right angle, since two right angles would already use 180°.
Can an isosceles triangle be obtuse?
Yes, when the vertex angle is greater than 90°. For example, a vertex angle of 120° leaves 30° for each base angle. The obtuse angle must be the vertex angle, because the base angles are equal and two obtuse angles cannot fit in one triangle.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 5.G.B.3, CCSS 5.G.B.4, CCSS HSG-CO.C.10
Cite this entry
Effortless Math Team. “Isosceles Triangle.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/isosceles-triangle/
Flashcard
TermIsosceles Triangletwo equal legs
DefinitionA triangle with at least two equal sides; the base angles are equal. Vertex 40° gives base angles 70° each.
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