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 is expressed as: a² + b² = c².

Front

In a right triangle, which side is the hypotenuse?

Back

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

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

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

Front

What is the formula to find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the formula: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the other sides.

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Front

If a right triangle has legs of lengths 6 cm and 8 cm, what is the length of the hypotenuse?

Back

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

Front

What does 'a' and 'b' represent in the Pythagorean Theorem?

Back

'a' and 'b' represent the lengths of the two legs of a right triangle.

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: 13² - 5² = 169 - 25 = 144; √144 = 12).

Front

True or False: The Pythagorean Theorem can be used to determine if a triangle is a right triangle.

Back

True. If a² + b² = c² holds true, then the triangle is a right triangle.

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.