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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the length of the missing side if one leg is 6 and the hypotenuse is 10?

Back

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

Front

Is a triangle with sides 9, 12, and 15 a right triangle?

Back

Yes (9² + 12² = 15²; 81 + 144 = 225; 225 = 225).

Front

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

Back

To find the length of a leg (a or b), use the formula: a² = c² - b² or b² = c² - a².

Front

If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Back

12 (Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

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 a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes (8² + 15² = 17²; 64 + 225 = 289; 289 = 289).