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 the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

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

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

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

How do you find a missing side of a right triangle if the hypotenuse and one side are known?

Back

Rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²), depending on which side is missing.

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 side opposite the 30° angle is the shortest.

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

If the hypotenuse of a right triangle is 10 cm and one side is 6 cm, what is the length of the other side?

Back

Using the Pythagorean Theorem: b = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

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

How can the Pythagorean Theorem be applied to find the distance between two points on a graph?

Back

By using the distance formula derived from the Pythagorean Theorem: d = √((x₂ - x₁)² + (y₂ - y₁)²).