Question: What name is given to a triangle with two equal sides?
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Isosceles.
A triangle with two sides of equal length is known as an “isosceles triangle.” Derived from the Greek words “isos” meaning “equal” and “skelos” meaning “leg,” the term aptly describes the triangle’s distinct feature of having two sides that are congruent, or of the same measure.
In an isosceles triangle, the two equal sides are termed the “legs,” while the third side, which is typically of a different length, is called the “base.” This triangular form has some interesting properties that set it apart from other triangle types:
- Angles: The angles opposite the equal sides, known as the “base angles,” are always congruent. This means that if you know the measure of one base angle, you immediately know the measure of the other. The third angle, called the “vertex angle,” is formed by the two equal sides and is typically different from the base angles.
- Symmetry: An isosceles triangle exhibits an axis of symmetry. If you were to draw a vertical line (an altitude) from the triangle’s apex (where the two equal sides meet) down to the base, it would bisect the base into two equal parts and create two smaller congruent triangles.
- Special Cases: While every equilateral triangle (a triangle with all sides and angles equal) is also an isosceles triangle, the reverse is not true. An equilateral triangle can be seen as a special case of the isosceles triangle.
The isosceles triangle has been studied extensively throughout history, playing a role in both ancient and modern mathematics. Its properties and characteristics make it a fundamental shape in the study of geometry.
