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 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

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths (a² + b² = c²).

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5.

Front

What is the distance formula in coordinate geometry?

Back

The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²).

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. The shortest side is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is the longest side.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you find the diagonal of a rectangle using the Pythagorean Theorem?

Back

To find the diagonal (d) of a rectangle with length (l) and width (w), use the formula: d = √(l² + w²).

Front

If a rectangular pool measures 30 m by 40 m, what is the diagonal distance across the pool?

Back

Using the Pythagorean Theorem: d = √(30² + 40²) = √(900 + 1600) = √2500 = 50 m.