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

The longest side of a right triangle is called the hypotenuse.

Front

If a triangle has sides a=3 and b=4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

Find the missing side: a=6, c=10. What is b?

Back

b = 8 (using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, b² = 64, b = √64 = 8).

Front

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

Back

The formula to find the hypotenuse (c) is c = √(a² + b²).

Front

A rectangular field is 30 yards wide and 40 yards long. How far is the diagonal?

Back

The diagonal is 50 yards (using the Pythagorean Theorem: √(30² + 40²) = √(900 + 1600) = √2500 = 50).

Front

If a triangle has sides a=8 and b=15, what is c?

Back

c = 17 (using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289, so c = √289 = 17).

Front

What do you call a triangle with one right angle?

Back

A triangle with one right angle is called a right triangle.

Front

In a right triangle, if one leg is 12 and the hypotenuse is 13, what is the other leg?

Back

The other leg is 5 (using the Pythagorean Theorem: 12² + b² = 13², so 144 + b² = 169, b² = 25, b = √25 = 5).

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 legs equals the square of the hypotenuse.