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: a² + b² = c².

Front

What does the Pythagorean Theorem help to find?

Back

The Pythagorean Theorem is used to find the lengths of missing sides in a right triangle.

Front

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

Back

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

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

Which set of sides forms a right triangle? 3, 4, 5 or 2, 2, 3?

Back

3, 4, 5 forms a right triangle (3² + 4² = 5²).

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

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

12 cm (Using the Pythagorean Theorem: 5² + b² = 13², 25 + b² = 169, b² = 144, b = 12).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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