Pythagoram Theorem Flashcard

Front

Side c on a right triangle is ALWAYS the longest.

Back

True. In a right triangle, the side opposite the right angle (hypotenuse) is always the longest side.

Front

Find the missing side: a = 48, b = 72. What is c?

Back

72. Using the Pythagorean theorem, c = √(a² + b²) = √(48² + 72²) = 72.

Front

Find the length of the missing side: a = 15, b = 13. What is c?

Back

13 cm. Using the Pythagorean theorem, c = √(a² + b²) = √(15² + 13²) = 13.

Front

This is a right triangle because —

Back

It has one 90 degree angle.

Front

What is a possible third side to a triangle with side lengths of 5 and 5?

Back

9. The third side must be less than the sum of the other two sides (5 + 5) and greater than their difference (5 - 5).

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): c² = a² + b².

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

10. Using the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

Can a triangle with sides 3, 4, and 5 be a right triangle?

Back

Yes. 3² + 4² = 5² (9 + 16 = 25), so it satisfies the Pythagorean theorem.

Front

What is the minimum length of the third side of a triangle with sides 5 and 5?

Back

1. The third side must be greater than the difference of the other two sides (5 - 5 = 0) and less than their sum (5 + 5 = 10).