Pythagoras theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the 'legs' (the two shorter sides) and the 'hypotenuse' (the longest side opposite the right angle).

Front

If one leg of a right triangle is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²).

Front

How do you find the length of a side if you know the hypotenuse and one leg?

Back

Rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and computer graphics to calculate distances and design structures.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem specifically applies to right triangles only.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse states that if in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.