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 longest side of a right triangle called?

Back

Hypotenuse.

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

In a right triangle, if the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

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

Front

True or False: The side 'a' in a right triangle is always the longest side.

Back

False.

Front

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

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has legs of lengths 5 cm and 12 cm, what is the length of the hypotenuse?

Back

13 cm (using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What do you call the two shorter sides of a right triangle?

Back

Legs.

Front

If the hypotenuse of a right triangle is 15 cm and one leg is 9 cm, what is the length of the other leg?

Back

√(15² - 9²) = √(225 - 81) = √144 = 12 cm.

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.