Pythagorean Theorem Flashcard

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

If one leg of a right triangle is 3 cm and the other leg 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

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

How do you find the length of the diagonal of a rectangle?

Back

Use the Pythagorean Theorem: if the width is w and the length is l, then the diagonal d can be found using d = √(w² + l²).

Front

What is the length of the diagonal of a rectangle that is 90 meters wide and 120 meters long?

Back

150 meters (Using the Pythagorean Theorem: √(90² + 120²) = √(8100 + 14400) = √22500 = 150).

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.

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 leg is 6 cm, what is the length of the other leg?

Back

8 cm (Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8).