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

In a right triangle, what is the hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you calculate the distance between two points in a coordinate plane?

Back

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 units.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining distances, constructing buildings, and designing triangular structures.

Front

What is the significance of the 3-4-5 triangle in geometry?

Back

The 3-4-5 triangle is a special right triangle where the sides are in the ratio 3:4:5. It is often used as a simple way to create a right angle.

Front

What is the diagonal of a rectangle with length 36 meters and width 18 meters?

Back

The diagonal can be calculated using the Pythagorean Theorem: d = √(36² + 18²) = √(1296 + 324) = √1620 ≈ 40.2 meters.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem).