Isosceles Triangle Hypotenuse

When the two sides of the triangle are said to be equal then the triangle is called as isosceles triangle. When all the sides of the triangle are equal then the triangle is called as the equilateral triangle and when no sides of the triangle are equal then it is said to be scalene triangle. In an isosceles triangle only the sides but also the two angles are said to be equal.
                                                               
Here we will see about the isosceles triangle hypotenuse.

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Isosceles triangle hypotenuse.

The hypotenuse side of the isosceles triangle is the sides that are found opposite to that of the right angle. According to the right angle theorem the height of the isosceles triangle is given by
                         h = √(b² – ¼ a²)
Thus the area of an isosceles triangle is
                        A = ½ ah
                            = ½ a √(b² – ¼ a²)
                            = ½ a² √((b²/a²) – (¼))
An isosceles triangle is also called as the triangle with two congruent sides. The angles which are opposite to these congruent sides are called as the base angles and the angles found between those sides are called as the vertex angle of the isosceles triangle.
Any equilateral triangle can be an isosceles triangle but no isosceles triangle is an equilateral triangle.                           

Properties of the isosceles triangle base:

• According to the right angle theorem the sum of the squares of the hypotenuse side is equal to the sum of the squares of the other two sides. The hypotenuse side is the side which is opposite to the right angle

• The side which is not equal to the other sides of a triangle is called as the base of the isosceles triangle.

• The base angles of the isosceles triangle are found to be equal.

• When the third angle of the isosceles triangle is a right angle then it is called as the right isosceles triangle.

• The perpendicular distance from the base to the vertex of an isosceles triangle is called as the altitude of the isosceles triangle.

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