KnowraIsosceles triangleIsosceles triangleA triangle with at least two sides of equal length. Its angles opposite those sides are equal.BriefConnectTriangle: A polygon with three sides and three interior angles. An isosceles triangle is a triangle distinguished by equal side lengths.Line of symmetry: A line that divides a figure into two mirror-image halves. The line through the apex and base midpoint reflects one half of an isosceles triangle onto the other.Compass-and-straightedge construction: A geometric construction using only an unmarked straightedge and a compass. Copying a segment length constructs an isosceles triangle from a chosen base.Right isosceles triangle: An isosceles triangle with one right angle and two 45° angles. It combines equal legs with a right angle, giving a particularly simple side ratio.Base angles theorem: The theorem that angles opposite equal sides in a triangle are equal. It states the defining angle relationship of an isosceles triangle.Altitude of a triangle: A perpendicular segment from a triangle's vertex to the opposite side or its extension. The apex altitude in an isosceles triangle also bisects the base and apex angle.Perpendicular bisector: A line perpendicular to a segment at its midpoint. Every point on this line is equally distant from the base's endpoints, allowing an isosceles triangle to be constructed.Obtuse isosceles triangle: An isosceles triangle with one angle greater than 90°. Its equal base angles must both be acute, leaving the apex angle obtuse.Equilateral triangle: A triangle with three sides of equal length and three equal angles. It is the special case in which all three sides, not just two, are equal.Pythagorean theorem: A theorem stating that the squares of a right triangle's legs sum to the square of its hypotenuse. The altitude splits the triangle into right triangles whose side lengths can be calculated with this theorem.Show all 20Linked from 18 pagesOrthocenterBroader topic: Its symmetry axis contains the orthocenter.Morley's trisector theoremRelated: Its reflection symmetry makes two of the three trisector intersections correspond.Inscribed angle theoremNarrower topic: Radii form isosceles triangles that explain the angle relationship.Euler lineBroader topic: Its symmetry axis contains the circumcenter, centroid, and orthocenter, so it is also its Euler line.Constant chord theoremRelated: Two radii and a chord form an isosceles triangle, linking a chord to its central angle.Van Schooten's theoremNarrower topic: Joining P to the triangle’s vertices creates isosceles triangles that expose equal base angles.Euler's inequalityBroader topic: Its symmetry makes the relationship between its inradius and circumradius easy to inspect.Exterior angle theoremBroader topic: Its equal remote angles make the exterior angle twice either base angle.Show all 18