Definition: An isosceles triangle is a triangle with two sides of equal length.
Key Properties:
* Two equal sides: This is the defining characteristic.
* Two equal angles: The angles opposite the equal sides are also equal.
* Angle-Side-Angle (ASA) Congruence: If two triangles have two corresponding angles and the included side equal, then the triangles are congruent. This is particularly useful for proving properties about isosceles triangles.
* Base angles: The angles opposite the equal sides are often called base angles.
* Vertex angle: The angle formed by the two equal sides is called the vertex angle.
* Line of symmetry: An isosceles triangle has a line of symmetry that bisects the vertex angle and the base.
* Altitude bisects the base: The altitude drawn from the vertex angle to the base bisects the base and is also the perpendicular bisector.
Important Note: While an equilateral triangle is a special case of an isosceles triangle (all sides equal), the term "isosceles" specifically refers to triangles with *at least* two equal sides.
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