Pythagorean Theorem (3B)

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

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

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 relationship between the sides of a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers (a, b, c) that satisfy the equation a² + b² = c². For example, (3, 4, 5) is a Pythagorean triple.

Front

Can the numbers 9, 5, and 6 form a Pythagorean triple?

Back

No, because 9² + 5² = 81 + 25 = 106, which is not equal to 6² (36).

Front

What is the formula to check if three numbers can form a right triangle?

Back

To check if three numbers a, b, and c can form a right triangle, verify if a² + b² = c², where c is the largest number.

Front

If the lengths of two sides of a right triangle are 6 mm and 8 mm, what is the length of the third side?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 mm.

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

How can the Pythagorean Theorem be applied in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the height of a ladder against a wall or the distance between two points on a map.