An isosceles triangle is a type of triangle that has at least two sides of equal length. These equal sides are known as the legs of the triangle, and the third side is called the base. Isosceles triangles are significant in geometry due to their unique properties and symmetry.
Key Properties of Isosceles Triangles
- The angles opposite the equal sides (legs) are also equal. These are called the base angles.
- The altitude (height) drawn from the vertex (the point where the legs meet) to the base is also a median and an angle bisector. It divides the triangle into two congruent right triangles and the base into two equal segments.
- The vertex angle is the angle formed by the two legs of the triangle.
Examples of Isosceles Triangles
Example 1: In an isosceles triangle with sides of lengths 5 cm, 5 cm, and 8 cm, the base is the side measuring 8 cm. The base angles, opposite the equal sides, are congruent.
Example 2: If an isosceles triangle has a vertex angle of 40 degrees, then each base angle is (180 – 40) / 2 = 70 degrees, since the sum of angles in any triangle is 180 degrees.
Applications of Isosceles Triangles
Isosceles triangles are used in various fields, including architecture, engineering, and art, due to their symmetry and properties. They are also fundamental in the study of triangle congruence and similarity in geometry.
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