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The Right angled triangle in geometry

A right angled triangle is a type of triangle which has one angle that is equal to 90 degrees. The other two angles are less than 90 degrees. A right angled triangle is also called a right triangle or a rectangular triangle. The side of a triangle which is opposite to the right angle is called the hypotenuse. It is the longest side of the triangle. The other two sides are called the legs or catheti of the triangle.

The Pythagorean theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem is represented by the equation: a^2 + b^2 = c^2 . This theorem is named after Pythagoras, who was a Greek mathematician. He lived in the 6th century BC.

The theorem can be used to find the length of any one side if the lengths of the other two sides are known. It can also be used to check if three given lengths could represent the sides of a right angled triangle.

There are several different types of right angled triangles. They include:

-Scalene Right Angled Triangle: All three sides are unequal in length.

-Isosceles Right Angled Triangle: Two sides are equal in length.

-Equilateral Right Angled Triangle: All three sides are equal in length. This means that it is also an equiangular triangle as all three angles are equal (to 90 degrees).

-Right Isosceles Triangle: A special case where not only do two sides have equal lengths, but these lengths also happen to be the length of the hypotenuse! This means that angle C must be 45 degrees (as it's complementary angle will sum up to 90 with it).

Conclusion

A right angled triangle is a geometrical figure with interesting properties and applications in real life situations. In this blog post, we have explored what a right angled triangle is and some different types of right angled triangles. We have also looked at how to use Pythagoras' theorem to calculate unknown side lengths. Next time you see a right angled triangle, you will know some things about them!

FAQ

Which best describes a right triangle?

A right triangle is a type of triangle which has one angle that is equal to 90 degrees. The other two angles are less than 90 degrees.

How do you prove a right triangle in geometry?

The Pythagorean theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is represented by the equation: a^2 + b^2 = c^2 .

What is a right triangle called?

A right angled triangle is also called a right triangle or a rectangular triangle. The side of a triangle which is opposite to the right angle is called the hypotenuse. It is the longest side of the triangle. The other two sides are called the legs or catheti of the triangle.