Mastering Isosceles Triangles: Properties, Formulas, And Applications

isoceles triangle

a triangle that has at least 2 congruent (equal) sides

An isosceles triangle is a triangle with two sides of equal length and two equal internal angles. In an isosceles triangle, the two equal sides are called the legs, and the third side is known as the base.

Properties of an Isosceles Triangle:
– Two sides are equal in length
– Two internal angles are equal
– The angles opposite the equal sides are equal
– The base angles (the angles formed between the base and the legs) are equal
– The median that passes through the base is also an altitude

Formulas related to an Isosceles Triangle:
– The Pythagorean Theorem can be used to find the length of the base, b, in terms of the length of the legs, a: b = √(4a^2 – c^2)/2
– The area of an isosceles triangle can be found using the formula: A = (1/2)bh, where b is the length of the base, and h is the height (the perpendicular distance between the base and the vertex opposite the base).
– The perimeter of an isosceles triangle can be found by adding the lengths of all three sides: P = 2a + b. Since two sides are the same, the perimeter can also be written as P = 2a + 2b.

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