Flashcard Pythagorean Theory

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the 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

The hypotenuse is 5 cm, calculated using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √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 Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

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

The length of the other leg is 8 cm, calculated as follows: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

Can the Pythagorean Theorem be used for obtuse triangles?

Back

No, the Pythagorean Theorem cannot be used for obtuse triangles.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of 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

The hypotenuse is 13 cm, calculated using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169, so c = √169 = 13.