Flashcards on Pythagoras Theorem

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What is the Pythagoras Theorem?

The Pythagoras Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

What are the three sides of a right triangle?

The three sides of a right triangle are the hypotenuse, adjacent, and opposite.

What is the formula for Pythagoras Theorem?

The formula for Pythagoras Theorem is c² = a² + b², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

What is the Pythagorean triple?

The Pythagorean triple is a set of three positive integers, (a, b, c), that satisfy the equation a² + b² = c².

Can any triangle be a right triangle?

No, only a triangle with one angle of 90 degrees can be a right triangle.

What is the hypotenuse of a right triangle?

The hypotenuse of a right triangle is the longest side, which is opposite to the right angle.

What is a right-angled triangle?

A right-angled triangle is a triangle in which one of the angles is 90 degrees.

What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees.

What is the Pythagorean theorem used for in real life?

The Pythagorean theorem is used in various fields like architecture, engineering, astronomy, navigation, and physics, to calculate measurements, distances or areas.

What are the three Pythagorean triples less than 20?

The three Pythagorean triples less than 20 are (3, 4, 5), (5, 12, 13), and (8, 15, 17).

How is the Pythagorean Theorem proven?

The Pythagorean Theorem can be proven using Euclid's Proposition 47 or by using algebraic methods.

What is the Pythagorean identity in trigonometry?

The Pythagorean identity in trigonometry is sin²θ + cos²θ = 1, for any angle θ.

What is the history of the Pythagorean Theorem?

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited for its discovery.

What is the difference between the Pythagorean Theorem and the distance formula?

The Pythagorean Theorem is a special case of the distance formula in two dimensions, while the distance formula can be generalized to more complex geometries.

What is the inverse of the Pythagorean Theorem?

The inverse of the Pythagorean Theorem is the Law of Cosines, which relates the cosine of an angle to the lengths of the sides of a triangle.

What is the Pythagoras Theorem?

The Pythagoras Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

What are the three sides of a right triangle?

The three sides of a right triangle are the hypotenuse, adjacent, and opposite.

What is the formula for Pythagoras Theorem?

The formula for Pythagoras Theorem is c² = a² + b², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

What is the Pythagorean triple?

The Pythagorean triple is a set of three positive integers, (a, b, c), that satisfy the equation a² + b² = c².

Can any triangle be a right triangle?

No, only a triangle with one angle of 90 degrees can be a right triangle.

What is the hypotenuse of a right triangle?

The hypotenuse of a right triangle is the longest side, which is opposite to the right angle.

What is a right-angled triangle?

A right-angled triangle is a triangle in which one of the angles is 90 degrees.

What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees.

What is the Pythagorean theorem used for in real life?

The Pythagorean theorem is used in various fields like architecture, engineering, astronomy, navigation, and physics, to calculate measurements, distances or areas.

What are the three Pythagorean triples less than 20?

The three Pythagorean triples less than 20 are (3, 4, 5), (5, 12, 13), and (8, 15, 17).

How is the Pythagorean Theorem proven?

The Pythagorean Theorem can be proven using Euclid's Proposition 47 or by using algebraic methods.

What is the Pythagorean identity in trigonometry?

The Pythagorean identity in trigonometry is sin²θ + cos²θ = 1, for any angle θ.

What is the history of the Pythagorean Theorem?

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited for its discovery.

What is the difference between the Pythagorean Theorem and the distance formula?

The Pythagorean Theorem is a special case of the distance formula in two dimensions, while the distance formula can be generalized to more complex geometries.

What is the inverse of the Pythagorean Theorem?

The inverse of the Pythagorean Theorem is the Law of Cosines, which relates the cosine of an angle to the lengths of the sides of a triangle.

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