Isosceles Triangle Calculator
Two equal sides, two equal angles
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Isosceles Triangle
About Isosceles Triangles
An isosceles triangle has two sides of equal length (called legs or equal sides) and two equal angles (called base angles). The third side is called the base.
Key Properties
- Two sides are equal in length
- Two base angles are equal
- The height from the vertex angle bisects the base
- The height creates a line of symmetry
- Base angles + vertex angle = 180°
Formulas
- Height: h = √(a² - b²/4)
- Area: A = (b × h) / 2
- Perimeter: P = 2a + b
- Vertex angle: θ = 180° - 2α (where α is base angle)
Frequently Asked Questions
What makes a triangle isosceles?
A triangle is isosceles if it has at least two sides of equal length. This automatically means it also has two equal angles.
Which angles are equal in an isosceles triangle?
The two base angles (opposite the equal sides) are always equal. The vertex angle (between the equal sides) is typically different.
Can an isosceles triangle be a right triangle?
Yes, an isosceles right triangle has two equal sides and angles of 45°, 45°, and 90°.
How do I find the height of an isosceles triangle?
Use h = √(a² - b²/4) where a is the equal side and b is the base. The height bisects the base at a right angle.
Is an equilateral triangle also isosceles?
Yes, an equilateral triangle is a special case of an isosceles triangle where all three sides are equal (not just two).
What is the line of symmetry?
The line of symmetry is the height drawn from the vertex angle to the base. It divides the isosceles triangle into two congruent right triangles.
Can the base be longer than the equal sides?
Yes, the base can be longer or shorter than the equal sides, as long as it satisfies the triangle inequality (sum of any two sides greater than the third).
How many lines of symmetry does an isosceles triangle have?
An isosceles triangle has exactly one line of symmetry, running from the vertex angle to the midpoint of the base.