Is the square of the hypotenuse is always equal to the sum of the squares of the two legs in a right triangle?

Is the square of the hypotenuse is always equal to the sum of the squares of the two legs in a right triangle?

Yes. Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

What theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs of a right triangle?

Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

How do you find the square of the hypotenuse?

The hypotenuse is the longest side and it’s always opposite the right angle. In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

What does the Pythagorean theorem say about the areas of the squares on the sides of a right angle triangle?

Pythagoras Theorem Squares As per the Pythagorean theorem, the area of the square which is built upon the hypotenuse of a right triangle is equal to the sum of the area of the squares built upon the other two sides. These squares are known as Pythagoras squares.

Is the hypotenuse equal to the sum of the other two sides?

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

What is converse Pythagorean Theorem?

The converse of the Pythagorean Theorem says that if a triangle has sides of length a, b, and c and if a^2 + b^2 = c^2 then the angle opposite the side of length c is a right angle.

What is PGT theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

What is meant by the square of the hypotenuse?