Pythagorean 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 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the length of one leg of a right triangle if the hypotenuse and the other leg are known?

Back

The formula is: a = √(c² - b²) or b = √(c² - a²), where c is the hypotenuse and a and b are the legs.

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 can the Pythagorean Theorem be used in real life?

Back

The Pythagorean Theorem can be used in various real-life applications such as construction, navigation, and determining distances.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x1, y1) and (x2, y2) is: d = √((x2 - x1)² + (y2 - y1)²).

Front

If the hypotenuse of a right triangle is 13 cm and one leg is 5 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(13² - 5²); b = √(169 - 25); b = √144; b = 12 cm.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it establishes a relationship between the sides of right triangles, which is essential for various geometric proofs and applications.