5-1 The Pythagorean Theorem (Flashcardizz)

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

If one side of a right triangle is 5 cm and the other side is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.

Front

Which set of sides can form a right triangle? 4, 5, 6 or 5, 12, 13?

Back

The set 5, 12, 13 can form a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

What is the length of the missing side if one side is 9 cm and the hypotenuse is 15 cm?

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 15² = 9² + b². So, 225 = 81 + b², which gives b² = 144. Therefore, b = √144 = 12 cm.

Front

If the lengths of the two legs of a right triangle are 8 cm and 15 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17 cm.

Front

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

Back

In a right triangle, the relationship is defined by the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

Find the length of the missing side if one side is 24 cm and the hypotenuse is 26 cm.

Back

Using the Pythagorean Theorem: 26² = 24² + b². So, 676 = 576 + b², which gives b² = 100. Therefore, b = √100 = 10 cm.

Front

What is the value of c if a = 7 cm and b = 24 cm?

Back

Using the Pythagorean Theorem: c² = 7² + 24² = 49 + 576 = 625. Therefore, c = √625 = 25 cm.

Front

If the hypotenuse is 30 cm and one leg is 18 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 30² = 18² + b². So, 900 = 324 + b², which gives b² = 576. Therefore, b = √576 = 24 cm.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (3, 4, 5).