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An isosceles triangle is a triangle that has any two of their sides to be equal to one another. Also, the opposite angles of this triangle are equal; in general terms, a triangle is a polygon that has three sides as well as vertices. The sides and the angles of this triangle could vary. The kinds of triangles can be divided on the basis of the sides and angles. Based on such sides, a triangle is successfully classified into three kinds namely, scalene, isosceles and equilateral. Whereas, on the basis of angles, a triangle is known to be of three kinds too, namely, acute angled, right angled and obtuse angled.

Isosceles triangle has two equal sides that are opposite to one another. In other words, it can be said that an isosceles triangle is a triangle that has two congruent sides. For instance, in a triangle △ABC, if sides AB and AC are equal to each other, then △ABC is an isosceles triangle where in ∠ B will be equal to ∠ C. The theorem which describes the isosceles triangle is “if two sides of a triangle are potentially congruent, then the angle that would be opposite to them are also congruent.”

The triangle that has all 3 sides equal is called an equilateral triangle; also, the triangle that has all three sides not equal is the scalene triangle.

- Since the 2 sides are equal in this triangle, the unequal side is known as the base of the triangle.
- The angles which are opposite to the two equal sides of the triangle will always be equal.
- The altitude of an isosceles triangle is always measured from the base of the triangle to the vertex of the triangle which is the topmost point of the triangle.
- All the right isosceles triangle has their third angle as the right angle which is always 90 degrees.

Usually, isosceles triangle is divided into different kinds namely the isosceles acute triangle, isosceles right triangle and isosceles obtuse triangle. Isosceles triangle has dimensions of legs, base and height and it has an axis of symmetry along the perpendicular bisector of the base. Relying on the angle in between the 2 legs, the isosceles triangle is divided as acute, right and obtuse. An isosceles triangle is acute if two of the opposite angles of a triangle are equal and are less than 90 degrees. A right isosceles triangle, as discussed has 2 equal sides wherein one of those two sides act as the hypotenuse and the other one acts as the base of the triangle. The third side is the unequal and it is the hypotenuse of the triangle. Here the famous Pythagoras theorem can be applied wherein the square of the hypotenuse would be equal to the sum of the square of the base as well as the perpendicular. For instance, the sides of the right isosceles triangle are a, a, and h, where a represents the two equal sides and h is the hypotenuse, then the formula would be written as follows:

**h = √(a2 + a2) = √2a2 = a√2**

or, to be stated in simple terms, it can be written as h = √2 a.

It is commonly known that the obtuse triangle in which one of the angle is greater than 90 degrees of the right angle. Also, it is not completely possible to draw a triangle with more than two angles that are obtuse. It is also known that an obtuse triangle can be an isosceles or a scalene triangle. Hence, the isosceles triangle is the triangle, which has two equal sides with an obtuse angle.

The area of an isosceles triangle is described as the region occupied by it in the 2D space. In general terms, the isosceles triangle is half the product of the height and the base of an isosceles triangle. The formula for the calculation of area of an isosceles triangle is as follows: **A = ½ × b × h Square units; **A representing Area of the isosceles triangle. As for the perimeter of the shape which is the boundary of the shape, it is defined as the sum of the 3 sides of an isosceles triangle. The perimeter of an isosceles triangle can be calculated if the base and the side is known; therefore, the formula is as follows: **P = 2a + b units; **where P represents the perimeter of an isosceles triangle and **a** is the length of the isosceles triangle and **b **is the base of the triangle. Whenever an altitude is drawn to the base of the isosceles triangle, it bisects the vertex angle. While it bisects the base, the 2 congruent triangles are created. The altitude of the triangle forms the necessary right angle and the altitude becomes the congruent hypotenuse. Hence, the altitude of drawn to the base of an isosceles bisects the base of the triangle.

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